At what speed should the electron revolve around the nucleus of a hydrogen atom in order that it may not be pulled into the nucleus by electrostatic attraction? Take the radius of orbit of an electron as 0.5 Å , the mass of the electron as 9.1× 10- 31kg and charge as 1.6× 10- 19 C .

Question

At what speed should the electron revolve around the nucleus of a hydrogen atom in order that it may not be pulled into the nucleus by electrostatic attraction? Take the radius of orbit of an electron as 0.5 Å , the mass of the electron as 9.1× 10- 31kg and charge as 1.6× 10- 19 C . (A) 2.25× 104 ms- 1 (B) 2.25× 105 ms- 1 (C) 2.25× 106 ms- 1 (D) 2.25× 107 ms- 1

Tardigrade Admin · Accepted Answer

For motion of the electron around the nucleus, (m v2/r)=(1/4 π ϵ 0) .(e . e/r2) ⇒ v2=(1/4 π ϵ 0) .(e2/m r) ⇒ v2=(9 × 109 ×(1.6 × 10-19)2/9.1 × 10-31 × 0.5 × 10-10)=5 × 1012 ⇒ v≈ 2.25× 106 m s- 1

$2.25 \times 1 0^{4} m s^{- 1}$

$2.25 \times 1 0^{5} m s^{- 1}$

$2.25 \times 1 0^{6} m s^{- 1}$

$2.25 \times 1 0^{7} m s^{- 1}$

Q. At what speed should the electron revolve around the nucleus of a hydrogen atom in order that it may not be pulled into the nucleus by electrostatic attraction? Take the radius of orbit of an electron as 0.5Å , the mass of the electron as 9.1×10−31kg and charge as 1.6×10−19C .

2.25×104ms−1

2.25×105ms−1

2.25×106ms−1

2.25×107ms−1

For motion of the electron around the nucleus, rmv2​=4πϵ0​1​.r2e.e​ ⇒v2=4πϵ0​1​.mre2​ ⇒v2=9.1×10−31×0.5×10−109×109×(1.6×10−19)2​=5×1012 ⇒v≈2.25×106ms−1

$2.25 \times 1 0^{4} m s^{- 1}$

$2.25 \times 1 0^{5} m s^{- 1}$

$2.25 \times 1 0^{6} m s^{- 1}$

$2.25 \times 1 0^{7} m s^{- 1}$