The ratio of speed of electrons in the first excited state of hydrogen atom to the speed of light in vacuum is [Given, Planck's constant =6.625 10⁻³⁴ Js and permittivity of free space is 8.85 10⁻¹² Fm ⁻¹ ]

Step-by-step solution

Velocity of electron in the nth orbit of an atom is given by v= 2 k e^2 h Z n where, 2 k e^2 h is a constant quantity and Z is atomic number. Hence, speed of electron in first excited state (n = 2) is aligned v & =2.188 10^6 1 2 (Z=1, for hydrogen atom ) & =1.094 10^6 ~ms ⁻¹ aligned Ratio of speed of electron in lst excited state to aligned the speed of light in vacuum & = 1.094 10^6 3 10^8 & =0.364 10⁻² & =3.6 10⁻³ aligned