Question

calculate <r2> for the first stage of hydrogen atom

Answer 1

We can use following formula

ke²/r² = mv²/r ....(1)

where ke²/r² is the Coulomb's force and mv²/r is the centripetal force of the electron around the nucleus.

Also Bohr's postulate is as follows

mvr = nh/2π (2)

v = nh /2 pi m r put this value in (1) inshort combine equation (1) and (2) we will get as follows

ke²/r² = (mn²h²) / (r⁴ pi m²r²)

r = n²h²/k4 pi²me²

In above equation put

Plank's constant h= 6.624 10^-34 Js

electron mass m_e= 9.11 10^-31 Kg

electron charge e= -1.6 10^-19 C

Coulomb's constant k=8.99 10⁹ m²N/C²

r = 0.53 Angstrom

r^2 = 0.2809 Angstrom^2