Question

The number of times larger the spacing between the energy levels with n = 3 and n = 8 spacing between the energy level with n = 8 and n = 9 for the hydrogen atom is ______.

Options

• 3.23

• 4.98

• 5.23

• 6.74

Answer 1

The number of times larger the spacing between the energy levels with n = 3 and n = 8 spacing between the energy level with n = 8 and n = 9 for the hydrogen atom is 3.23.

Explanation:

r₁ = `0.529 ["n"_1^2/"z" - "n"_2^2/"z"]`

= 0.529 × [8² – 3²]

= 29.095 Å

r₂ = 0.529 × (9² – 8²)

= 8.9 Å

`"r"_1/"r"_2 = 29.095/8.9` = 3.23 ....(spacing)