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Atoms and Nuclei

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Q 1. Consider {tex} \alpha {/tex} particles, {tex} \beta {/tex} particles and {tex} \gamma {/tex}-rays, each having an energy of {tex}0.5 \mathrm{MeV}.{/tex} In increasing order of penetrating powers, the radiations are:

{tex} \alpha , \beta , \gamma {/tex}

{tex} \alpha , \gamma , \beta {/tex}

{tex} \beta , \gamma , \alpha {/tex}

{tex} \gamma , \beta , \alpha {/tex}

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Q 2. The circuit shown in the figure contains two diodes each with a forward resistance of 50 ohms and with infinite backward resistance. If the battery voltage is 6 V, the current through the 100 ohm resistance (in amperes) is

Zero

0.02

0.03

0.036

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Q 3. Which of the following is a correct statement?

Beta rays are same as cathode rays

Gamma rays are high energy neutrons

Alpha particles are singly ionised helium atoms

Protons and neutrons have exactly the same mass

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Q 4. The electron in a hydrogen atom makes a transition from an excited state to the ground state. Which of the following statements is true?

Its kinetic energy increases and its potential and total energies decreases.

Its kinetic energy decreases, potential energy increases and its total energy remains the same.

Its kinetic and total energies decrease and its potential energy increases.

Its kinetic, potential and total energies decrease.

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Q 5. If an X-ray tube operates at the voltage of {tex} 10 \mathrm { kV } , {/tex} find the ratio of the de Broglie wavelength of the incident electrons to the shortest wavelength of {tex} \mathrm { X } {/tex} -rays produced. The specific charge of electron is {tex} 1.8 \times 10 ^ { 11 } \mathrm { C } \ \mathrm { kg } {/tex}

1

0.1

1.8

1.2

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Q 6. Figure represents some of the lower energy levels of the hydrogen atom in simplified form. If the transition of an electron from {tex} E _ { 4 } {/tex} to {tex} E _ { 2 } {/tex} were associated with the emission of blue light, which one of the following transitions could be associated with the emission of red light?

{tex} E _ { 4 } {/tex} to {tex} E _ { 1 } {/tex}

{tex} E _ { 3 } {/tex} to {tex} E _ { 1 } {/tex}

{tex} E _ { 3 } {/tex} to {tex} E _ { 2 } {/tex}

{tex} E _ { 1 } {/tex} to {tex} E _ { 3 } {/tex}

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Q 7. Which of the following statement is true regarding Bohr's model of hydrogen atom?

(I) Orbiting speed of an electrons decreases as it falls to discrete orbits away from the nucleus

(II) Radii of allowed orbits of electrons are proportional to the principal quantum number

(III) Frequency with which electrons orbit around the nucleus in discrete orbits is inversely proportional to the cube of principal quantum number

(IV) Binding force with which the electron is bound to the nucleus increase as it shifts to outer orbits.

Select the correct answer using the codes given below:

I and II

II and IV

I, II and III

II, III and IV

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Q 8. The electron in a hydrogen atom makes a transition from {tex} n = n _ { 1 } {/tex} to {tex} n = n _ { 2 } {/tex} state. The time period of the electron in the initial state is eight times that in the final state. The possible values of {tex} n _ { 1 } {/tex} and {tex} n _ { 2 } {/tex} are

{tex} n _ { 1 } = 4 , n _ { 2 } = 2 {/tex}

{tex} n _ { 1 } = 8 , n _ { 2 } = 2 {/tex}

{tex} n _ { 1 } = 8 , n _ { 2 } = 3 {/tex}

{tex} n _ { 1 } = 6 , n _ { 2 } = 2 {/tex}

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Q 9. Two hydrogen-like atoms {tex} A {/tex} and {tex} B {/tex} are of different and each atom has ratio of neutron to proton equal to unity. The difference in the energies between the first Lyman lines emitted by {tex} A {/tex} and {tex} B {/tex} is {tex} 81.6 \mathrm { eV } . {/tex} When the atoms {tex} A {/tex} and {tex} B {/tex} moving with the same velocity strike separately a heavy target, they rebound back with half of the speed before collision. However, in this process atom {tex} B {/tex} imparts the target a momentum which is three times the momentum imparted to target by atom {tex} A {/tex}

Atom {tex} A {/tex} is

{tex} _1^1\mathrm H {/tex}

{tex} _1^2\mathrm { H } {/tex}

{tex} ^6_3 \mathrm { Li } {/tex}

{tex} ^4_2\mathrm { Li } {/tex}

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Q 10. The fraction of a radioactive material which remains active after time {tex} t {/tex} is {tex} 9 / 16 . {/tex} The fraction which remains active after time {tex} t / 2 {/tex} will be

{tex} \frac { 4 } { 5 } {/tex}

{tex} \frac { 7 } { 8 } {/tex}

{tex} \frac { 3 } { 5 } {/tex}

{tex} \frac { 3 } { 4 } {/tex}

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Q 11. A radioactive sample {tex} S _ { 1 } {/tex} having an activity of {tex} 5 \mu \mathrm { Ci } {/tex} has twice the number of nuclei as another sample {tex} S _ { 2 } {/tex} which has an activity of {tex} 10 \mu \mathrm { Ci } {/tex}. The half lives of {tex} S _ { 1 } {/tex} and {tex} S _ { 2 } {/tex} can be

{tex} 20 \mathrm { yr } {/tex} and {tex} 5 \mathrm { yr } {/tex} respectively

{tex} 20 \mathrm { yr } {/tex} and {tex} 10 \mathrm { yr } {/tex} respectively

{tex} 10 \mathrm { yr } {/tex} each

{tex} 5 \mathrm { yr } {/tex} each

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Q 12. A sample of a radioactive element has a mass of {tex} 10 \mathrm { g } {/tex} at an instant {tex} t = 0 . {/tex} The approximate mass of this element in the sample after two mean lives is

{tex} 1.35 \mathrm g {/tex}

{tex} 2.50 \mathrm { g } {/tex}

{tex} 3.70 \mathrm g {/tex}

{tex} 6.30 \mathrm { g } {/tex}

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Q 13. A neutron of energy {tex}1\mathrm {MeV} {/tex} and mass {tex} 1.6 \times {/tex} {tex} 10 ^ { - 27 } \mathrm { kg } {/tex} passes a proton at such a distance that the angular momentum of the neutron relative to the proton approximately equals {tex} 10 ^ { - 33 } \mathrm { Js } {/tex}. The distance of closest approach neglecting the interaction between particles is

{tex} 0.44 \mathrm { nm } {/tex}

{tex} 0.44 \mathrm { mm } {/tex}

{tex} 0.44 {\text{Å}} {/tex}

{tex} 0.44 \mathrm { fm } {/tex}

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