Question

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?

Answer 1

The longest possible wavelength emitted by hydrogen atoms in visible range in such a world according to Bohr's model is 487 nm

Explanation:

• The angular momentum in the imaginary world is quantized to be an integral multiple that is even with h/2π.

• So, the allowed quantum numbers are n2 = 4 and n1 = 2.

• For minimum energy, the possible longest wavelength for least energy.

• The emitted light has the energy E and is shown as

• E = 13.61n12 - 1n22E = 13.6 × 1264 = 2.55 eV

• When the calculated energy is equated with the photo, we obtain:

• 2.55 eV = hcλλ = 12422.55 nm = 487 nm