Question

Let T₁ and T₂ be the energy of an electron in the first and second excited states of hydrogen atom, respectively. According to the Bohr’s model of an atom, the ratio T₁: T₂ is:

Options

• 1:4

• 4:1

• 4:9

• 9:4

Answer 1

9:4

Explanation:

For first excited state, n₁ = 2

And for second excited state, n₂ = 3

As,

\[T=-13.6\frac{Z^2}{n^2}\]

\[T_1=-13.6\times\frac{(1)^2}{(2)^2}\]

\[T_2=-13.6\times\frac{(1)^2}{(3)^2}\]

\[T_1{:}T_2=\frac{1}{4}:\frac{1}{9}=9{:}4\]