Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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Suppose in an Imaginary World the Angular Momentum is Quantized to Be Even Integral Multiples of H/2π. What is the Longest Possible Wavelength - Physics

Sum

Suppose in an imaginary world the angular momentum is quantized to be even integral multiples of h/2π. What is the longest possible wavelength emitted by hydrogen atoms in visible range in such a world according to Bohr's model?

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Solution

In the imaginary world, the angular momentum is quantized to be an even integral multiple of h/2 π.

Therefore, the quantum numbers that are allowed are n1 = 2 and n2 = 4

We have the longest possible wavelength for minimum energy.

Energy of the light emitted (E) is given by

`E = 13.6 (1/n_1^2 - 1/n_2^2)`

`E = 13.6 [ 1/(2)^2 - 1/(4)^2]`

`E = 13.6 (1/4 - 1/16)`

`E = (13.6xx12)/64 = 2.55  eV`

Equating the calculated energy with that of photon, we get

2.55 eV = `(hc)/lamda`

`lamda = (hc)/2.55 = 1242/2.55  nm`

= 487.05 nm= 487 nm

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APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 21 Bohr’s Model and Physics of Atom
Q 45 | Page 386
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