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Doubly ionised helium atoms and hydrogen ions are accelerated from rest through the same potential drop. The ratio of the final velocities of the helium and the hydrogen ion is [1994]
- a)1/2
- b)2
- c)1/√2
- d)√2
Correct answer is option 'D'. Can you explain this answer?
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Doubly ionised helium atoms and hydrogen ions are accelerated from res...
1/2 mv2 = eV, or, v = (2eV/m)1/2
the mass of helium ion is four times that of
hydrogen ion. Further, the charge on helium
ion is twice that of hydrogen ion.
hydrogen ion. Further, the charge on helium
ion is twice that of hydrogen ion.
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Doubly ionised helium atoms and hydrogen ions are accelerated from res...
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Doubly ionised helium atoms and hydrogen ions are accelerated from res...
The final velocity of an ion accelerated through a potential drop can be calculated using the formula:
vf = √(2qV/m)
where vf is the final velocity, q is the charge of the ion, V is the potential drop, and m is the mass of the ion.
For doubly ionized helium (He2+) and hydrogen (H+) ions, the charges are q = 2e and q = e, respectively, where e is the elementary charge. The masses are m = 4m_p and m = m_p, respectively, where m_p is the mass of a proton.
Therefore, the ratio of the final velocities is:
vf(He2+)/vf(H+) = √(2(2e)V/4m_p) / √(2eV/m_p)
Simplifying this expression, we get:
vf(He2+)/vf(H+) = √2
Therefore, the correct answer is (b) 2.
vf = √(2qV/m)
where vf is the final velocity, q is the charge of the ion, V is the potential drop, and m is the mass of the ion.
For doubly ionized helium (He2+) and hydrogen (H+) ions, the charges are q = 2e and q = e, respectively, where e is the elementary charge. The masses are m = 4m_p and m = m_p, respectively, where m_p is the mass of a proton.
Therefore, the ratio of the final velocities is:
vf(He2+)/vf(H+) = √(2(2e)V/4m_p) / √(2eV/m_p)
Simplifying this expression, we get:
vf(He2+)/vf(H+) = √2
Therefore, the correct answer is (b) 2.
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Doubly ionised helium atoms and hydrogen ions are accelerated from rest through the same potential drop. The ratio of the final velocities of the helium and the hydrogen ion is [1994]a)1/2b)2c)1/√2d)√2Correct answer is option 'D'. Can you explain this answer?
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Doubly ionised helium atoms and hydrogen ions are accelerated from rest through the same potential drop. The ratio of the final velocities of the helium and the hydrogen ion is [1994]a)1/2b)2c)1/√2d)√2Correct answer is option 'D'. 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 Doubly ionised helium atoms and hydrogen ions are accelerated from rest through the same potential drop. The ratio of the final velocities of the helium and the hydrogen ion is [1994]a)1/2b)2c)1/√2d)√2Correct answer is option 'D'. 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 Doubly ionised helium atoms and hydrogen ions are accelerated from rest through the same potential drop. The ratio of the final velocities of the helium and the hydrogen ion is [1994]a)1/2b)2c)1/√2d)√2Correct answer is option 'D'. Can you explain this answer?.
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