The deuteron is bound by nuclear forces just | vedclass

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

Question

(D) The binding energy of an $H$-atom is given by the formula:$E = \frac{m_e e^4}{8 \epsilon_0^2 h^2} = 13.6 	ext{ eV}$ ... $(1)$Now,considering the

Vedclass · Accepted Answer

$2.0$

Vedclass · Answer

(D) The binding energy of an $H$-atom is given by the formula:$E = \frac{m_e e^4}{8 \epsilon_0^2 h^2} = 13.6 	ext{ eV}$ ... $(1)$Now,considering the deuteron nucleus as a binary system,we replace $m_e$ with the reduced mass $m'$ and $e$ with the effective charge $e'$. The binding energy of the deuteron is:$E' = \frac{m' e'^4}{8 \epsilon_0^2 h^2} = 2.2 	imes 10^6 	ext{ eV}$ ... $(2)$Taking the ratio of equation $(2)$ to equation $(1)$:$\frac{m'}{m_e} 	imes \left(\frac{e'}{e}ight)^4 = \frac{2.2 	imes 10^6}{13.6} \approx 1.617 	imes 10^5$ ... $(3)$The reduced mass $m'$ of the deuteron (proton-neutron system) is:$m' = \frac{m_p m_n}{m_p + m_n} = \frac{m 	imes m}{2m} = \frac{m}{2}$Given $m \approx 1836 m_e$,we have $m' = \frac{1836 m_e}{2} = 918 m_e$.Thus,$\frac{m'}{m_e} = 918$.Substituting this into equation $(3)$:$918 	imes \left(\frac{e'}{e}ight)^4 = 1.617 	imes 10^5$$\left(\frac{e'}{e}ight)^4 = \frac{1.617 	imes 10^5}{918} \approx 176.14$$\frac{e'}{e} = (176.14)^{1/4} \approx 3.65$.

Similar Questions

If $M(A, Z)$,$M_p$,and $M_n$ represent the masses of the nucleus ${}_{Z}^{A}X$,proton,and neutron in $u$ units respectively $(1u = 931.5 \, MeV/c^2)$,and $BE$ represents the binding energy in $MeV$,then which of the following relations is correct?

$A$ given coin has a mass of $3.0\; g$. Calculate the nuclear energy that would be required to separate all the neutrons and protons from each other. For simplicity, assume that the coin is entirely made of $_{29}^{63} Cu$ atoms (of mass $62.92960\; u$).

The mass of a nucleus,a neutron,and a proton are $M$,$M_n$,and $M_p$ respectively. Then which of the following is true?

Which one of the following statements is correct?

The average binding energy per nucleon in the nucleus of an atom is approximately

Vedclass Test Series

Exam Paper Generator

Online Exam Module