Question

calculate the ratio of velocity of light and the velocity of electron in the 2nd orbit of hydrogen atom(h=-6.624×10^-8)

Answer 1

Velocity of electron in nth Both orbit can be given as v=(2πe2K)/h∗(Z/n)v=(2πe2K)/h∗(Z/n)m/s

Putting the values of the constants, the above expression becomes, v=2.18∗106∗(Z/n)v=2.18∗106∗(Z/n) m/s

Now according to your question, we need to find out the velocity of electron in 2nd orbit of hydrogen.

This implies, Z = 1 & n = 2 .

Which gives, v=2.18∗106∗(1/2)m/s=1.09∗106v=2.18∗106∗(1/2)m/s=1.09∗106 m/s .

We know that the speed of light is equal to 3*10^8 m/s .

Therefore, required ratio = (3∗108)/(1.09∗106)=275.23(3∗108)/(1.09∗106)=275.23 (approx.) .

Hope it clears your query.