Question

The ratio of the radius of the first Bohr orbit for the electron
orbiting the hydrogen nucleus to that of the electron orbiting
the deuterium nucleus (mass nearly twice that of the hydrogen
nucleus) is approximately
(a) 2 : 1 (b) 1 : 1
(c) 1 : 2 (d) 4 : 1

Answer 1

Option (b) is the answer since the radius is mass independent.

Answer 2

answer : option (b) 1 : 1

according to Bohr's model,

r = n²h²/4π²mKZe² = (h²/4π²mKe²) × n²/Z

here definitely mass is mentioned in formula of radius but this is electron mass rather than mass of atom. so, m is constant for all atom.

i.e., r ∝ n²/Z

in above question, in first case electron is revolving around the hydrogen nucleus and in 2nd case, it is revolving around the deuterium nucleus in same orbit.

but we know, deuterium is isotope of hydrogen.

so, Z = 1 for both hydrogen and deuterium.

and n is also same.

hence, r is also same for both cases.

so ratio of their radii is 1 : 1 .