Speed of electron in its lst Bohr's orbit is given by 2.18 × 106 ms -1. If the time period of electron in n th orbit is measured as 4.10 femto second, the value of n is

Question

Speed of electron in its lst Bohr's orbit is given by 2.18 × 106 ms -1. If the time period of electron in n th orbit is measured as 4.10 femto second, the value of n is (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

Given, speed of the electron in lst Bohr's orbit,

v_{1} = 2.18 \times 1 0^{6} m / s

Time period of

n

th orbit,

T_{n} = 4.10 f - s = 4.1 \times 1 0^{- 15} s

Radius of Bohr's first orbit,

r_{1} = 0.53 \times 1 0^{- 10} m

∴

Orbital period of electron in Bohr's first orbit,

T_{1} = \frac{2 π r _{1}}{v _{1}} = \frac{2 \times 3.14 \times 0.53 \times 1 0 ^{- 10}}{2.18 \times 1 0 ^{6}}

T_{1} = 1.52 \times 1 0^{- 16} s

Again, Time period of

n

th orbit is given by

T_{n} = n^{3} T_{1}

\Rightarrow n^{3} = \frac{T _{n}}{T _{1}} = \frac{4.1 \times 1 0 ^{- 15}}{1.52 \times 1 0 ^{- 16}} = 26.98

n^{3} = 27 \Rightarrow n = (27)^{1/3} \Rightarrow n = 3

Q. Speed of electron in its lst Bohr's orbit is given by 2.18×106ms−1. If the time period of electron in n th orbit is measured as 4.10 femto second, the value of n is

1

2

3

4

Q. Speed of electron in its lst Bohr's orbit is given by $2.18 \times 1 0^{6} m s^{- 1}$ . If the time period of electron in $n$ th orbit is measured as $4.10$ femto second, the value of $n$ is