In one model of the electron, the electron of mass me is thought to be a uniformly charged shell of radius R and to tal charge e, whose electrostatic energy E is equivalent to its mass me via Einstein’s mass energy relation E =mec2. In this model, R is approximately (me = 9.1 × 1031 kg, c = 3 ×108 ms-1, 1 / 4πε0 = 9 × 109 Fm-1, magnitude of the electron charge = 1.6 × 1019 C)

Question

In one model of the electron, the electron of mass me is thought to be a uniformly charged shell of radius R and to tal charge e, whose electrostatic energy E is equivalent to its mass me via Einstein’s mass energy relation E =mec2. In this model, R is approximately (me = 9.1 × 1031 kg, c = 3 ×108 ms-1, 1 / 4πε0 = 9 × 109 Fm-1, magnitude of the electron charge = 1.6 × 1019 C) (A) 14 ×10-15 m  (B) 2 ×10-13 m  (C) 5.3 ×10-11 m  (D) 2.8×10-35 m

Tardigrade Admin · Accepted Answer

Electrostatic energy of charged shell is E=(e2/8πε0R) and from Einsteinâs mass - energyequivalence, E = mc2 Equating both, we get (e2/8πε0R)=mc2 ⇒ Rv=(e2/8πε0 .mc2) Substituting values, we have ⇒ R= ((1.6 ×10-19)2×9×109/2×9.1×10-31×9×1016) =1.4×10-15 m

$14 \times 1 0^{- 15} m$

$2 \times 1 0^{- 13} m$

$5.3 \times 1 0^{- 11} m$

$2.8 \times 1 0^{- 35} m$

14×10−15m

2×10−13m

5.3×10−11m

2.8×10−35m

Electrostatic energy of charged shell is E=8πε0​Re2​ and from Einstein’s mass - energyequivalence, E=mc2 Equating both, we get 8πε0​Re2​=mc2 ⇒Rv=8πε0​.mc2e2​ Substituting values, we have ⇒R=2×9.1×10−31×9×1016(1.6×10−19)2×9×109​ =1.4×10−15m

$14 \times 1 0^{- 15} m$

$2 \times 1 0^{- 13} m$

$5.3 \times 1 0^{- 11} m$

$2.8 \times 1 0^{- 35} m$