CBSE Class 12 · 2011 · Modern PhysicsShort Answer

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(a) Using de-Broglie's hypothesis, explain with the help of a suitable diagram Bohr's second postulate of quantization of orbital angular momentum in a hydrogen atom.
(b) The ground state energy of a hydrogen atom is

- 13.6

eV. What are the kinetic and potential energies of the electron in this state?

Answer: $2 π r = nλ$ ; $K = 13.6$ eV, $U = - 27.2$ eV.

Solution

(a) Treating the orbiting electron as a standing matter wave, the orbit is stable only if its circumference contains a whole number of de-Broglie wavelengths:

2 π r = nλ = n \frac{h}{m v}

, which rearranges to Bohr's second postulate

m v r = \frac{nh}{2 π}

.
(b) For a bound electron,

K = - E

and

U = 2 E

K = - (- 13.6) = + 13.6 eV, U = 2 (- 13.6) = - 27.2 eV .

K = 13.6 eV, U = - 27.2 eV

CBSE Class 12 Board · 2011 · Subjective

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