Gamma Decay

Q. An electron in a hydrogen atom first jumps from third excited state to second excited state and then from second excited state to first excited state. The ratio of wavelengths ${\lambda }_1:{\lambda }_2$ emitted in the two cases is -

1. $\frac{7}{5}$
2. $\frac{27}{20}$
3. $\frac{5}{7}$
4. $\frac{20}{7}$

Q. The energy of a hydrogen atom in the first excited state, if the potential energy is assumed to be zero in the ground state is

1. $21.2eV$
2. $19.1eV$
3. $13.6eV$
4. $23.8eV$

Q.

A free hydrogen atom after absorbing a photon of wavelength ${\lambda }_a$ gets excited from the state $n=1$ to the state $n=4$. Immediately after that the electron jumps to n = m state by emitting a photon of wavelength ${\lambda }_e$. Let the change in momentum of atom due to the absorption and the emission are $\Delta P_a$ and $\Delta P_e$ respectively. If ${\lambda }_a/{\lambda }_e=1/5$, which of the option (s) is/are correct ?
[Use $hc=1242eV$ nm ; $1nm={10}^{-9}m$, h and c are Plank's constant and speed of light, respectively]

1. the ratio of kinetic energy of the electron in the state n = m to the state $n=1$ is $1/4$

2. $m=2$

3. $\Delta P_a/\Delta P_e=1/2$

4. ${\lambda }_e=418nm$

Q. A gamma ray photon creates an electron-positron pair. If the rest mass energy of an electron is 0.5 MeV and the total kinetic energy of the electron-positron pair is 0.78 MeV, then the energy of the gamma ray photon must be

1. 0.78 MeV
2. 1.78 MeV ​
3. 1.28 MeV ​
4. 0.28 MeV

Q. When an electron jumps from a radius n = $\infty$ to n = 2 of hydrogen atom then it radiates energy of the wavelength ____________nm. If required, use hc = 1242 eV.nm.
___

Q. Nuclear fission can be explained by

1. Collective model of the nucleus
2. Shell model of the nucleus.
3. Optical model of the nucleus.
4. Liquid drop model of the nucleus.

Q. Polonium ${(}_{84}{\text{Po}}^{210})$ emits ${}_2{\alpha }^4$ particles and is converted into lead ${(}_{82}{\text{Pb}}^{206})$. This reaction is used for producing electric power in a space mission. ${\text{Po}}^{210}$ has a half-life of $138.6\text{days}$. Assuming an efficiency of $10\%$ of the thermoelectric machine, how much ${\text{Po}}^{210}$ is required to produce $1.2\times {10}^7\text{J}$ of electric energy per day at the end of $693\text{days}$?

$\text{Given masses of the nuclei}{\text{Po}}^{210}=209.98264\text{amu},{\text{Pb}}^{206}=205.97440\text{amu},{\alpha }^4=4.00260\text{amu},1\text{amu}\times c^2=931\text{MeV}\text{Avogadro number=}6\times {10}^{23}.$

1. $10\text{g}$
2. $320\text{g}$
3. $640\text{g}$
4. $100\text{g}$

Q.

${}^{57}\text{Co}$ decays to ${}^{57}\text{Fe}$ by ${\beta }^{+}$ emission. The resulting ${}^{57}\text{Fe}$ is in its excited state and comes to the ground state by emitting $\gamma$ rays. The half-life of ${\beta }^{+}$ decay is 270 days and that of the $\gamma$ emission is ${10}^{-6}$ s. A sample of ${}^{57}\text{Co}$ gives 5.0$\times {10}^9$ gamma rays per second. How much time will elapse before the emission rate of gamma rays drops to 2.5 $\times {10}^9$

Q.

What is Potassium ionization energy?

Q. Identify the correct ascending order of $\alpha ,\beta \text{and}\gamma$ rays with reference to their ionizing power.
$\left(I\right)\alpha -ray$, $\left(II\right)\gamma -ray$, $\left(III\right)\beta -ray$

1. $II,III,I$
2. $I,III,II$
3. $II,I,III$
4. $I,II,III$

Q. An electromagnetic radiation has energy of 13.2 Kev, then radiation belongs to the region. 1.Microwave 2.X-ray 3.Infrared 4.Visible

Q. The half life period of a radioactive element A is the same as the mean life of another radioactive element B. Initially both of them have the same number of atoms. The radioactive element B decays faster than A. Explain why.

Q. A nucleus with $Z=92$, emits the following in a sequence, $\alpha ,{\beta }^{-},{\beta }^{-},\alpha ,\alpha ,\alpha ,\alpha ,\alpha ,{\beta }^{-},$ ${\beta }^{-},\alpha ,{\beta }^{+},{\beta }^{+},\alpha$. The $Z$ of the resulting nucleus is ______.

Q. Identify the correct order of $\alpha ,\beta$ and $\gamma$ with reference to their penetrating power in decreasing order. I) $\alpha$ -ray II) $\gamma$ -ray III) $\beta$ -ray

1. II, III, I
2. II, I, III
3. I, II, III
4. III, I, II

Q. Which of the following can produce electromagnetic waves?

1. A charge moving with uniform acceleration.
2. A charge moving with uniform retardation.
3. An oscillating charge.
4. All of the above

Q. A gamma ray photon creates an electron-positron pair. If the rest mass energy of an electron is $0.5MeV$ and the total kinetic energy of the electron-positron pair is $0.78MeV$, then the energy of the gamma ray photon must be

1. $1.78MeV$
2. $0.78MeV$
3. $1.28MeV$
4. $0.28MeV$

Q. The relation between energy and wavelength in an electromagnetic wave like gamma radiation is given by?

1. $E=hc/\lambda$
2. $E=hc\lambda$
3. There is no relationship
4. None of these

Q. Which element is best suited for target material in production of X-rays?

$Z$ is the atomic number.

$Z_A=13,Z_B=15,Z_C=20,Z_D=50$

1. $A$
2. $B$
3. $C$
4. $D$

Q. At time $t=0$, a radioactive sample has a mass of $10g$. Calculate the expected mass of radioactive sample after two successive mean lives.

Q. The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, ${\lambda }_1/{\lambda }_2$ of the photons emitted in this process is:

1. $\frac{9}{7}$
2. $\frac{7}{5}$
3. $\frac{20}{7}$
4. $\frac{27}{5}$

Q. Using the equation $N=N_0{e}^{-\lambda T}$, obtain the relation between half-life $\left(\lambda \right)$ and decay, constant (A) of a radioactive substance.

Q. The decay constant of ²³⁸U is 4.9 × 10⁻¹⁸ S⁻¹. (a) What is the average-life of ²³⁸U? (b) What is the half-life of ²³⁸U? (c) By what factor does the activity of a ²³⁸U sample decrease in 9 × 10⁹ years?

Q. The total energy of an electron in the ground state of hydrogen atom is $-13.6eV$. The potential energy of an electron in the ground state of $L{i}^{2+}$ ion will be

1. $122.4eV$
2. $-122.4eV$
3. $-244.8eV$
4. $244.8eV$

Q. What is the maximum energy of the anti-neutrino?

1. Zero
2. Much less than $0.8\times {10}^{6}eV$
3. Nearly $0.8\times {10}^{6}eV$
4. Much larger than $0.8\times {10}^{6}eV$

Q. The phenomenon of pair production is :

1. The production of an electron and a positron from $\gamma$ radiation
2. Ejection of an electron from a metal surface when exposed to ultraviolet light
3. Ionization of a neutral atom
4. Ejection of an electron from a nucleus

Q. Assertion :Statement I: Though the light of a single frequency (monochromatic light) is incident metal, the energies omitted photoelectrons are different. Reason: Statement Il: The energy of electrons just after they absorb photons incident on the metal surface may be lost a collision with other atoms in the metal before the electron is ejected out of the metal.

1. Statement I is True, Statement Il is True; Statement Il is a correct explanation for Statement I.
2. Statement I is True, Statement Il is True; Statement Il is NOT a correct explanation for Statement I.
3. Statement I is True, Statement Il is False.
4. Statement I is False, Statement Il is True.

Q. A photon, an electron and an uranium nucleus all have the same wavelength. The one which has the minimum energy ?

1. Is the photon
2. Is the electron
3. Is the uranium nucleus
4. Depends upon the wavelength and the prperties of the particle

Q. Assertion :$\gamma$-radiation emission occurs after $\alpha$ and $\beta$ decay. Reason: Energy levels occur in nucleus.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
3. Assertion is correct but Reason is incorrect.
4. Both Assertion and Reason are incorrect.

Q. ${}_{83}^{214}Bi\underset{}{\overset{\alpha -emission}{\to }}A\underset{}{\overset{\beta -emission}{\to }}B\underset{}{\overset{\beta -emission}{\to }}C\underset{}{\overset{\beta -emission}{\to }}D\underset{}{\overset{\alpha -emission}{\to }}E$
'$E$' is an element of stable nucleus. What is the element '$E$'?

1. ${}_{82}^{206}Pb$
2. ${}_{80}^{206}Hg$
3. ${}_{81}^{207}Tl$
4. ${}_{79}^{206}Au$

Q. a) Three types of radioactive decay occur in nature. Briefly describe them.
b) State the law of radio active decay.