Question
The radius of the second Bohr orbit for hydrogen atom is :
( Plank's const. $$h = 6.6262 \times {10^{ - 34}}Js;$$ mass of electron $$ = 9.1091 \times {10^{ - 31}}kg;$$ charge of electron $$e = 1.60210 \times {10^{ - 19}}C$$ permittivity of vaccum $${}^ \in 0 = 8.854185 \times {10^{ - 12}}k{g^{ - 1}}{m^{ - 3}}{A^2})$$
A.
$$1.65\mathop {\text{A}}\limits^{\text{o}} $$
B.
$$4.76\mathop {\text{A}}\limits^{\text{o}} $$
C.
$$0.529\mathop {\text{A}}\limits^{\text{o}} $$
D.
$$2.12\mathop {\text{A}}\limits^{\text{o}} $$
Answer :
$$2.12\mathop {\text{A}}\limits^{\text{o}} $$
Solution :
Radius of nth Bohr orbit in H-atom
$$ = 0.53\,{n^2}\mathop {\text{A}}\limits^{\text{o}} $$
Radius of 2nd Bohr orbit $$ = 0.53 \times {\left( 2 \right)^2}$$
$$ = 2.12\mathop {\text{A}}\limits^{\text{o}} $$