Home
Class 12
PHYSICS
The electrostatic energy of Z protons un...

The electrostatic energy of `Z` protons uniformly distributed throughout a spherical nucleus of radius `R` is given by
`E = (3 Z(Z- 1)e^(2))/5( 4 pi e _(0)R)`
The measured masses of the neutron `_(1)^(1) H, _(7)^(15) N and , _(8)^(16)O are 1.008665 u, 1.007825 u , 15.000109 u and 15.003065 u, ` respectively Given that the ratio of both the `_(7)^(12) N` and `_(8)^(15) O` nucleus are same , 1 u = = 931.5 Me V`c^(2) ` (c is the speed of light ) and `e^(2)//(4 pi e_(0)) = 1.44 MeV` fm Assuming that the difference between the binding energies of `_7^(15) N and `_(8)^(15) O ` is purely due to the electric energy , The radius of the nucleus of the nuclei is

A

2.85 fm

B

3.03 fm

C

3.42 fm

D

3.80 fm

Text Solution

Verified by Experts

The correct Answer is:
C
Electrosta tic energy = `BE_(N) -BE_(O)`
= `[ 7M_(p) +8M_(n) -M_(N)]-[8M_(p)+7M_(n) -M_(O)]c^(2)`
`=[-M_(p)+M_(n)+M_(O) -M_(N)]c^(2)`
`=[-1.007825 +1.008665 +15.003065 - 15.000109]`
` xx 931 .5` MeV
= `3.5359` MeV
`DeltaE = 3/5 xx(1.44 xx 8xx7)/R -3/5 xx(1.44 xx 7 xx 6)/R = 3.5359`
` rArr R = 3.42 ` fm .
Promotional Banner

Similar Questions

Explore conceptually related problems

The electrotatic energy of Z protons uniformly distributed throughout a spherical nucleus of ratio R is given by E = (3 Z(Z- 1)e^(2))/(5 4 pi e _(0)R) The measured masses of the neutron _(1)^(1) H, _(7)^(15) N and , _(8)^(15)O are 1.008665 u, 1.007825 u , 15.000109 u and 15.003065 u, repectively Given that the ratio of both the _(7)^(12) N and _(8)^(15) O nu8cles are same , 1 u = = 931.5 Me Vc^(2) (c is the speed of light ) and e^(2)//(4 p-i e^_(0)) = 1.44 MeV fm Assuming that the difference between the binding e4nergies of _(7_^(15) N and _(8)^(15) O is puraly due to the electric energy , The radius of the nucleas of the nuclei is

Show that the nuclide .^8Be has a positive binding energy but is unstable with respect to decay into two alpa particles, where masses of neutron, .^1H , and .^8 Be are 1.008665 u, 1.007825 u , and 8.005305 u , respectively.

The binding energy of ._(10)Ne^(20) is 160.6 MeV. Find its atomic mass. Take mass of proton =1.007825 u and mass of neutron =1.008665 u.

The masses of neutron and proton are 1.0087 a.m.u. and 1.0073 a.m.u. respectively. If the neutrons and protons combine to form a helium nucleus (alpha particle) of mass 4.0015 a.m.u. The binding energy of the helium nucleus will be (1 a.m.u. = 931 MeV) .

The masses of neutron and proton are 1.0087 a.m.u. and 1.0073 a.m.u. respectively. If the neutrons and protons combine to form a helium nucleus (alpha particles) of mass 4.0015 a.m.u. The binding energy of the helium nucleus will be (1 a.m.u.= 931 MeV)

Calculate the molecular masses of the following: (i) C_(12)H_(22)O_(11) , (ii) Al_(2)(SO_(4))_(3) Given atomic masses : C = 12.0 u, H= 1.0 u, O = 16.0 u, Al = 27.0 u, S = 32.0 u

The binding energy per nucleon of ""_(7)N^(14) nucleus is: (Mass of ""_(7)N^(14) = 14.00307 u ) mass of proton = 1.007825 u mass of neutron = 1.008665 u

Calculate the binding energy per nucleon in the nuclei of ._(15)P^(31) . Given m(._(15)P^(31))=30.97376u, m(._(0)n^(1))=1.00865 u, m(._(1)H^(1))=1.00782u .