Question

Hydrogen atom in n = 3 state has a lifetime of 10^-10 sec. The number of revolutions an electron makes in the n = 3 state before returning to the ground state is ______.

Useful data

`1/(4pi∈_0) = 8.99 xx 10^-34`N m² C^-2; e = 1.60 10^-19 C; h = 6.63  10^-34 Js; m_e = 9 × 10^-3 kg

विकल्प

• 2.4 × 10⁵

• 1.2 × 10⁵

• 2.4 × 10⁴

• 1.2 × 10⁴

Answer 1

Hydrogen atom in n = 3 state has a lifetime of 10^-10 sec. The number of revolutions an electron makes in the n = 3 state before returning to the ground state is 2.4 × 10⁴.

Explanation:

Given, 

Life time of hydrogen atom = 10^-10 S

Time period of electron, T = `(2pi"r")/"v"`

`= (2pix(0.529 xx 10^-10) xx 9 xx 3)/(2.18 xx 10^6)`

In 10^-10 S, number of revolution, electron will make

`= (10^-10 xx 2.18 xx 10^6)/(2pi xx 0.529 xx 27 xx 10^-10)`

`= (2.18 xx 10^6)/89.69`

`= (2.18 xx 10^5)/9`

`= 0.24 xx 10^5 = 2.4 xx 10^4`