CBSE Class 12 · 2018 · Modern PhysicsShort Answer

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(a) State Bohr's postulate to define stable orbits in a hydrogen atom. How does de-Broglie's hypothesis explain the stability of these orbits?
(b) A hydrogen atom initially in the ground state absorbs a photon which excites it to the

n = 4

level. Estimate the frequency of the photon.

Answer: $2 π r = nλ$ (standing wave); $ν \approx 3.1 \times 1 0^{15} Hz$ .

Solution

(a) Bohr's postulate: only those orbits are stable (non-radiating) for which the angular momentum is an integral multiple of

\frac{h}{2 π}

m v r = \frac{nh}{2 π}

.
De-Broglie's hypothesis explains this: the electron is a matter wave, and an orbit is stable only if its circumference contains a whole number of wavelengths (

2 π r = nλ

), forming a non-radiating standing wave (see figure).
(b) Energy absorbed:

Δ E = 13.6 (1 - \frac{1}{4 ^{2}}) = 13.6 \times \frac{15}{16} = 12.75 eV = 2.04 \times 1 0^{- 18} J .

ν = \frac{Δ E}{h} = \frac{2.04 \times 1 0 ^{- 18}}{6.63 \times 1 0 ^{- 34}} \approx 3.08 \times 1 0^{15} Hz .

ν \approx 3.1 \times 1 0^{15} Hz

CBSE Class 12 Board · 2018 · Subjective

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CBSE Class 12 · 2018 · Modern PhysicsShort Answer

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