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Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): de-Broglie wavelength of a gas molecule is inversely proportional to the square root of temperature.
Reason (R): The root mean square velocity of gas molecules depends on temperature.
- a)Both A and R are true and R is the correct explanation of A
- b)Both A and R are true but R is NOT the correct explanation of A
- c)A is true but R is false
- d)A is false and R is true
Correct answer is option 'A'. Can you explain this answer?
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Directions : In the following questions, A statement of Assertion (A)...
So, vRMS ∝ √T Again de-Broglie wavelength, λ = h/mv
So, λ ∝ 1/√T
Hence, assertion and reason both are true and reason explains the assertion.
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Directions : In the following questions, A statement of Assertion (A)...
**Assertion (A):** The de-Broglie wavelength of a gas molecule is inversely proportional to the square root of temperature.
**Reason (R):** The root mean square velocity of gas molecules depends on temperature.
The correct answer is option 'A'. Let's understand why.
**Explanation:**
**De-Broglie Wavelength (λ):**
- According to de-Broglie's hypothesis, every particle with momentum exhibits wave-like properties.
- The de-Broglie wavelength (λ) is the wavelength associated with a moving particle and is given by the equation λ = h/p, where h is Planck's constant and p is the momentum of the particle.
**Root Mean Square Velocity (v_rms):**
- The root mean square velocity of gas molecules is a measure of the average velocity of the gas particles.
- It is given by the equation v_rms = √(3RT/M), where R is the gas constant, T is the temperature, and M is the molar mass of the gas.
**Inversely Proportional Relationship:**
- The de-Broglie wavelength (λ) and the root mean square velocity (v_rms) are related to each other.
- According to the kinetic theory of gases, the average kinetic energy of gas molecules is directly proportional to the temperature.
- The kinetic energy of a gas molecule is given by the equation KE = (1/2)mv^2, where m is the mass of the gas molecule and v is its velocity.
- As the temperature increases, the average kinetic energy of the gas molecules increases, resulting in an increase in their velocity.
- Since the de-Broglie wavelength is inversely proportional to the momentum (λ = h/p), an increase in velocity leads to a decrease in the de-Broglie wavelength.
- Therefore, the de-Broglie wavelength of a gas molecule is inversely proportional to the square root of the temperature.
**Conclusion:**
- The root mean square velocity of gas molecules depends on the temperature, as stated in Reason (R).
- The de-Broglie wavelength of a gas molecule is inversely proportional to the square root of temperature, as stated in Assertion (A).
- Reason (R) provides the correct explanation for Assertion (A), as the increase in temperature leads to an increase in the velocity of gas molecules, resulting in a decrease in their de-Broglie wavelength.
**Reason (R):** The root mean square velocity of gas molecules depends on temperature.
The correct answer is option 'A'. Let's understand why.
**Explanation:**
**De-Broglie Wavelength (λ):**
- According to de-Broglie's hypothesis, every particle with momentum exhibits wave-like properties.
- The de-Broglie wavelength (λ) is the wavelength associated with a moving particle and is given by the equation λ = h/p, where h is Planck's constant and p is the momentum of the particle.
**Root Mean Square Velocity (v_rms):**
- The root mean square velocity of gas molecules is a measure of the average velocity of the gas particles.
- It is given by the equation v_rms = √(3RT/M), where R is the gas constant, T is the temperature, and M is the molar mass of the gas.
**Inversely Proportional Relationship:**
- The de-Broglie wavelength (λ) and the root mean square velocity (v_rms) are related to each other.
- According to the kinetic theory of gases, the average kinetic energy of gas molecules is directly proportional to the temperature.
- The kinetic energy of a gas molecule is given by the equation KE = (1/2)mv^2, where m is the mass of the gas molecule and v is its velocity.
- As the temperature increases, the average kinetic energy of the gas molecules increases, resulting in an increase in their velocity.
- Since the de-Broglie wavelength is inversely proportional to the momentum (λ = h/p), an increase in velocity leads to a decrease in the de-Broglie wavelength.
- Therefore, the de-Broglie wavelength of a gas molecule is inversely proportional to the square root of the temperature.
**Conclusion:**
- The root mean square velocity of gas molecules depends on the temperature, as stated in Reason (R).
- The de-Broglie wavelength of a gas molecule is inversely proportional to the square root of temperature, as stated in Assertion (A).
- Reason (R) provides the correct explanation for Assertion (A), as the increase in temperature leads to an increase in the velocity of gas molecules, resulting in a decrease in their de-Broglie wavelength.
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Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): de-Broglie wavelength of a gas molecule is inversely proportional to the square root of temperature.Reason (R): The root mean square velocity of gas molecules depends on temperature.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is trueCorrect answer is option 'A'. Can you explain this answer?
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Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): de-Broglie wavelength of a gas molecule is inversely proportional to the square root of temperature.Reason (R): The root mean square velocity of gas molecules depends on temperature.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is trueCorrect answer is option 'A'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): de-Broglie wavelength of a gas molecule is inversely proportional to the square root of temperature.Reason (R): The root mean square velocity of gas molecules depends on temperature.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is trueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): de-Broglie wavelength of a gas molecule is inversely proportional to the square root of temperature.Reason (R): The root mean square velocity of gas molecules depends on temperature.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is trueCorrect answer is option 'A'. Can you explain this answer?.
Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): de-Broglie wavelength of a gas molecule is inversely proportional to the square root of temperature.Reason (R): The root mean square velocity of gas molecules depends on temperature.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is trueCorrect answer is option 'A'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): de-Broglie wavelength of a gas molecule is inversely proportional to the square root of temperature.Reason (R): The root mean square velocity of gas molecules depends on temperature.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is trueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): de-Broglie wavelength of a gas molecule is inversely proportional to the square root of temperature.Reason (R): The root mean square velocity of gas molecules depends on temperature.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is trueCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): de-Broglie wavelength of a gas molecule is inversely proportional to the square root of temperature.Reason (R): The root mean square velocity of gas molecules depends on temperature.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is trueCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 12.
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Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): de-Broglie wavelength of a gas molecule is inversely proportional to the square root of temperature.Reason (R): The root mean square velocity of gas molecules depends on temperature.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is trueCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): de-Broglie wavelength of a gas molecule is inversely proportional to the square root of temperature.Reason (R): The root mean square velocity of gas molecules depends on temperature.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is trueCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): de-Broglie wavelength of a gas molecule is inversely proportional to the square root of temperature.Reason (R): The root mean square velocity of gas molecules depends on temperature.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is trueCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): de-Broglie wavelength of a gas molecule is inversely proportional to the square root of temperature.Reason (R): The root mean square velocity of gas molecules depends on temperature.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is trueCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Class 12 tests.
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