Speed of electron in its Ist Bohr's orbit is given by (2.18 10^6 ~ms ⁻¹ ). If the time period of electron in (n )th orbit is measured as 4.10 femto second, the value of (n ) is

Step-by-step solution

Given, speed of the electron in 1st Bohr's orbit, (v₁=2.18 10^6 ~m / s ) Time period of (n )th orbit, (T_n=4.10 f - s =4.1 10⁻¹⁵ ~s ) Radius of Bohr's first orbit, (r₁=0.53 10⁻¹⁰ ~m ) ( ) Orbital period of electron in Bohr's first orbit, ( aligned & T₁= 2 r₁ v₁ = 2 314 0.53 10⁻¹⁰ 2.18 10^6 & T₁=1.52 10⁻¹⁶ ~s aligned ) Again, Time period of (n )th orbit is given by ( aligned T_n & =n^3 T₁ n^3 & = T_n T₁ = 4.1 10⁻¹⁵ 1.52 10⁻¹⁶ =26.98 n^3 & =27 n=(27)^ 1 / 3 n=3 aligned )