Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12

# 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?

#### 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

Is there an error in this question or solution?

#### 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