In an atom, two electrons move around the nucleus in circular orbits of radii R and 4R. The ratio of the time taken by them to complete one revolution is :-

Question

In an atom, two electrons move around the nucleus in circular orbits of radii R and 4R. The ratio of the time taken by them to complete one revolution is :- (A) 1/4 (B) 4/1 (C) 8/1 (D) 1/8

Tardigrade Admin · Accepted Answer

T 2 propto (Radius of the orbit) 3 ∴ ( T 12/ T 22)=( R 3/(4 R )3)=(1/64) or ( T 1/ T 2)=(1/8)

Q. In an atom, two electrons move around the nucleus in circular orbits of radii $R$ and $4 R$ . The ratio of the time taken by them to complete one revolution is :-

1/4

4/1

8/1

1/8

$T^{2} \propto$ (Radius of the orbit) $^{3}$
$∴ \frac{T _{1}^{2}}{T _{2}^{2}} = \frac{R ^{3}}{( 4 R ) ^{3}} = \frac{1}{64}$
or $\frac{T _{1}}{T _{2}} = \frac{1}{8}$

Q. In an atom, two electrons move around the nucleus in circular orbits of radii R and 4R. The ratio of the time taken by them to complete one revolution is :-

1/4

4/1

8/1

1/8

T2∝ (Radius of the orbit) 3 ∴T22​T12​​=(4R)3R3​=641​ or T2​T1​​=81​

Q. In an atom, two electrons move around the nucleus in circular orbits of radii $R$ and $4 R$ . The ratio of the time taken by them to complete one revolution is :-

$T^{2} \propto$ (Radius of the orbit) $^{3}$
$∴ \frac{T _{1}^{2}}{T _{2}^{2}} = \frac{R ^{3}}{( 4 R ) ^{3}} = \frac{1}{64}$
or $\frac{T _{1}}{T _{2}} = \frac{1}{8}$