Mass Energy Equivalence

Q. A particle of mass $4M$, initially at rest, disintegrates into two particles of masses $M$ and $3M$, respectively, having non-zero velocities. The ratio of de-Broglie wavelength of the particle of mass $M$, to that of mass $3M$, will be,

1. $3:1$
2. $1:1$
3. $1:\sqrt{3}$
4. $1:3$

Q. 54 Suppose a pure Si crystal has 5*10 to the power 28 atoms per m3. It is doped by 1ppm concentration of pentavalent As. Calculate the number of electrons and holes. Given that ni =1.5*10 to the power 16 per m3.

Q. Obtain the binding energy (in MeV) of a nitrogen nucleus ( )147 N , given m ( )147 N =14.00307 u

Q. A body of mass $2M$ splits into four masses $m,M-m,m,M-m,$ which are rearranged to form a square as shown in the figure. The ratio of $\frac{M}{m}$ for which, the gravitational potential energy of the system becomes maximum is $x:1$. The value of $x$ is .

Q.

What is the average binding energy of a nucleus?

1. 8 eV

2. 8 keV

3. 8 BeV

4. 8 MeV

Q.

What is the mass of any kind of object that travels at the speed of light?

Q. One gram of hydrogen is converted into $0.993\text{grams}$ of helium in a thermonuclear reaction. The energy released is

1. $63\times {10}^7\text{J}$
2. $63\times {10}^{10}\text{J}$
3. $63\times {10}^{14}\text{J}$
4. $63\times {10}^{20}\text{J}$

Q.

Explain the law of conservation of energy.

Q. One cubic meter of mild steel weighs about

1. $1000kg$
2. $3625kg$
3. $7850kg$
4. $12560kg$

Q.

${}_{92}{}^{238}\mathrm{U}$ is known to undergo radioactive decay to form ${}_{82}{}^{206}\mathrm{Pb}$ by emitting alpha particles and beta particles. A rock initially contained $68\times {10}^{-6}\mathrm{g}$ of${}_{92}{}^{238}\mathrm{U}$. If the number of alpha particles that it would emit during its radioactive decay of ${}_{92}{}^{238}\mathrm{U}$ to ${}_{82}{}^{206}\mathrm{Pb}$ in three half-lives is $\mathrm{Z}\times {10}^{18}$then what is the value of Z?

Q.

The SI and CGS units of energy are joule and erg respectively. How many ergs are equal to one joule?

Q. Why is energy released when binding energy increases?

Q. A nucleus at rest undergoes a decay, emitting an $\alpha$ particle of de-Broglie wavelength $\lambda =5.76\times {10}^{-15}\text{m}$. If the mass of the daughter nucleus is $223.610\text{u}$ and that of the $\alpha -$ particle is $4.002\text{u}$, the mass of the parent nucleus in $\text{amu}$ nearly is (integer only)

Take : $1\text{u}=931.5\text{MeV}/c^{2}h=6.62\times {10}^{-34}\text{J s}$

Q.

According to Einsteins theory, mass and energy are related as _________.

Q.

Theory of relativity reveals that mass can be converted into energy. The energy E so obtained is proportional to certain powers of mass m and the speed c of light. Guess a realtion among the quantities using the method of dimensions.

Q.

The area of cross-section, length, and density of a piece of a metal of atomic weight 60 are 10^-6 m², 1.0 m and 5 x 10³ kgm^-3 respectively. The number of free electrons per unit volume if every atom contributes one free electron is

1. 5 x 10³⁰ m^-3

2. 8 x 10²⁸ m^-3

3. 4 x 10²¹ m^-3

4. 5 x 10²⁸ m^-3

Q.

What are the five types of radioactive decay?

Q. If a Hydrogen nucleus is completely converted into energy, the energy produced will be around

1. 1 MeV
2. 931 MeV
3. 9.38 MeV
4. 238 MeV

Q.

State the energy changes in a burning coal.

Q. An electron, an alpha particle, a proton and a neutron have same de-Broglie wavelength. What would be the order of their kinetic energies ?

1. $K.E_e>K.E_p>K.E_n>K.E_{\alpha }$
2. $K.E_{\alpha }>K.E_n>K.E_p>K.E_e$
3. $K.E_p=K.E_n=K.E_{\alpha }=K.E_e$
4. $K.E_p>K.E_n>K.E_{\alpha }>K.E_e$

Q.

What is $E=m{c}^2$ ?

Q. A nucleus $A$, with a finite de Broglie wavelength ${\lambda }_A$, undergoes spontaneous fission into two nuclei $B$ and $C$ of equal masses. $B$ flies in the same direction as that of $A$, while $C$ flies in the opposite direction with a velocity equal to half of that of $B$. The de Broglie wavelengths ${\lambda }_B$ and ${\lambda }_C$ of $B$ and $C$ are, respectively,

1. ${\lambda }_A,\frac{{\lambda }_A}{2}$
2. $\frac{{\lambda }_A}{2},{\lambda }_A$
3. $2{\lambda }_A,{\lambda }_A$
4. ${\lambda }_A,2{\lambda }_A$

Q. A given coin has a mass of 3.0 g. Calculate the nuclear energy thatwould be required to separate all the neutrons and protons fromeach other. For simplicity assume that the coin is entirely made of6329Cu atoms (of mass 62.92960 u).

Q.

Total energy always remains same

1. True
2. False

Q. Half life of a radioactive element is $5\text{min. and}10\text{sec}$. The time taken for $90\%$ of it to disintegrate is nearly,
(Given: ${\log }_{10}2=0.301$)

1. ${10}^4\text{min}$
2. ${10}^4\text{sec}$
3. ${10}^3\text{sec}$
4. ${10}^3\text{min}$

Q. A heavy nucleus having mass number $200$ gets disintegrated into two small fragments of mass number $80$ and $120$. If binding energy per nucleon for parent atom is $6.5MeV$ and for daughter nuclei is $7MeV$ and $8MeV$ respectively, then the energy released in the decay will be:

1. $200MeV$
2. $-220MeV$
3. $220MeV$
4. $180MeV$

Q. Supposing the I.P. of hydrogen atom is 960 eV. Find out the value of principal quantum number having the energy equal to -60 eV. 1) n=2 2) n=3 3) n=4 4) n=5

Q. Determine the amount of $\begin{array}{c}210\\ 84\end{array}Po$ (in micrograms) necessary to provide a source of alpha particles of $5$ millicurie strength. The half life of polonium is 138 days.

Q. The velocity of a body of rest mass $m_0$ is (where c is the velocity of light in vacuum). The mass of this body is

1. 
2. 
3. 
4. 

Q.

Find the separation between two massive particles each of mass $5\text{mg}$ if they experience a gravitational force of $6.66\text{dyne}$.