A 7.9 text{ MeV} alpha-particle scatters from | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) At the distance of closest approach $(r)$, the entire kinetic energy of the $\alpha$-particle is converted into electrostatic potential energy.By

Vedclass · Accepted Answer

$5.76 	imes 10^{-14}$

Vedclass · Answer

(A) At the distance of closest approach $(r)$, the entire kinetic energy of the $\alpha$-particle is converted into electrostatic potential energy.By the principle of conservation of mechanical energy:$K.E._i + P.E._i = K.E._f + P.E._f$Given $K.E._i = 7.9 	ext{ MeV} = 7.9 	imes 10^6 	imes 1.6 	imes 10^{-19} 	ext{ J}$, $P.E._i = 0$, $K.E._f = 0$, and $P.E._f = \frac{1}{4 \pi \epsilon_0} \frac{(2e)(Ze)}{r}$.$7.9 	imes 10^6 	imes 1.6 	imes 10^{-19} = \frac{9 	imes 10^9 	imes 2 	imes 79 	imes (1.6 	imes 10^{-19})^2}{r}$Solving for $r$:$r = \frac{9 	imes 10^9 	imes 2 	imes 79 	imes 1.6 	imes 10^{-19}}{7.9 	imes 10^6} = 2.88 	imes 10^{-14} 	ext{ m}$The diameter of the nucleus is $D = 2r = 2 	imes 2.88 	imes 10^{-14} = 5.76 	imes 10^{-14} 	ext{ m}$.

Similar Questions

In a Geiger-Marsden experiment,what is the distance of closest approach to the nucleus of a $7.7 \;MeV$ $\alpha$-particle before it comes momentarily to rest and reverses its direction?

The size of an atom is of the order of:

An $\alpha$-particle of $5 \; MeV$ energy strikes a stationary uranium nucleus at a scattering angle of $180^o$. The distance of closest approach of the $\alpha$-particle to the nucleus will be of the order of:

In Rutherford's experiment,the number of particles scattered at a $90^{\circ}$ angle is $x$ per second. The number of particles scattered per second at an angle of $60^{\circ}$ is:

The distance of the closest approach of an alpha particle fired at a nucleus with kinetic energy $K$ is $r_{0}$. The distance of the closest approach when the $\alpha$-particle is fired at the same nucleus with kinetic energy $2K$ will be . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module