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The wavelength (in nanometer) associated with a proton (mass = 1.67 x 10-27 kg atom-1) at the velocity of 1.0 x 103 ms-1 is
- a)0.032 nm
- b)0.4 nm
- c)2.500 nm
- d)4.000 nm
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The wavelength (in nanometer) associated with a proton (mass = 1.67 x ...
By de-Broglie’s equation
Most Upvoted Answer
The wavelength (in nanometer) associated with a proton (mass = 1.67 x ...
Understanding Wavelength Calculation
To find the wavelength associated with a proton, we use the de Broglie wavelength formula:
De Broglie Wavelength Formula:
- λ = h / p
Where:
- λ is the wavelength,
- h is Planck's constant (6.626 x 10^-34 Js),
- p is the momentum of the proton (p = mv).
Calculating Momentum (p):
- Mass of proton (m) = 1.67 x 10^-27 kg
- Velocity (v) = 1.0 x 10^3 m/s
Now, calculate momentum (p):
- p = mv = (1.67 x 10^-27 kg) * (1.0 x 10^3 m/s)
- p = 1.67 x 10^-24 kg m/s
Calculating Wavelength (λ):
- Now substitute the values into the de Broglie equation:
- λ = h / p
- λ = (6.626 x 10^-34 Js) / (1.67 x 10^-24 kg m/s)
Performing the Calculation:
- λ = 3.96 x 10^-10 m
- Convert meters to nanometers:
- λ = 3.96 x 10^-10 m * (1 x 10^9 nm/m) = 0.396 nm
This can be approximated to 0.4 nm (option b).
Conclusion:
- Therefore, the correct answer is option 'B': 0.4 nm, which represents the wavelength associated with the proton at the given velocity.
Key Takeaway:
- The de Broglie wavelength calculation provides insight into the wave-particle duality of matter, even for massive particles like protons.
To find the wavelength associated with a proton, we use the de Broglie wavelength formula:
De Broglie Wavelength Formula:
- λ = h / p
Where:
- λ is the wavelength,
- h is Planck's constant (6.626 x 10^-34 Js),
- p is the momentum of the proton (p = mv).
Calculating Momentum (p):
- Mass of proton (m) = 1.67 x 10^-27 kg
- Velocity (v) = 1.0 x 10^3 m/s
Now, calculate momentum (p):
- p = mv = (1.67 x 10^-27 kg) * (1.0 x 10^3 m/s)
- p = 1.67 x 10^-24 kg m/s
Calculating Wavelength (λ):
- Now substitute the values into the de Broglie equation:
- λ = h / p
- λ = (6.626 x 10^-34 Js) / (1.67 x 10^-24 kg m/s)
Performing the Calculation:
- λ = 3.96 x 10^-10 m
- Convert meters to nanometers:
- λ = 3.96 x 10^-10 m * (1 x 10^9 nm/m) = 0.396 nm
This can be approximated to 0.4 nm (option b).
Conclusion:
- Therefore, the correct answer is option 'B': 0.4 nm, which represents the wavelength associated with the proton at the given velocity.
Key Takeaway:
- The de Broglie wavelength calculation provides insight into the wave-particle duality of matter, even for massive particles like protons.
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The wavelength (in nanometer) associated with a proton (mass = 1.67 x 10-27 kg atom-1) at the velocity of 1.0 x 103 ms-1 isa)0.032 nmb)0.4 nmc)2.500 nmd)4.000 nmCorrect answer is option 'B'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The wavelength (in nanometer) associated with a proton (mass = 1.67 x 10-27 kg atom-1) at the velocity of 1.0 x 103 ms-1 isa)0.032 nmb)0.4 nmc)2.500 nmd)4.000 nmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The wavelength (in nanometer) associated with a proton (mass = 1.67 x 10-27 kg atom-1) at the velocity of 1.0 x 103 ms-1 isa)0.032 nmb)0.4 nmc)2.500 nmd)4.000 nmCorrect answer is option 'B'. Can you explain this answer?.
The wavelength (in nanometer) associated with a proton (mass = 1.67 x 10-27 kg atom-1) at the velocity of 1.0 x 103 ms-1 isa)0.032 nmb)0.4 nmc)2.500 nmd)4.000 nmCorrect answer is option 'B'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The wavelength (in nanometer) associated with a proton (mass = 1.67 x 10-27 kg atom-1) at the velocity of 1.0 x 103 ms-1 isa)0.032 nmb)0.4 nmc)2.500 nmd)4.000 nmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The wavelength (in nanometer) associated with a proton (mass = 1.67 x 10-27 kg atom-1) at the velocity of 1.0 x 103 ms-1 isa)0.032 nmb)0.4 nmc)2.500 nmd)4.000 nmCorrect answer is option 'B'. Can you explain this answer?.
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