Nuclei Test

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Nuclei Test - 45

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following assertions are correct?

A
A neutron can decay to a proton only inside a nucleus

B
A proton can change to a neutron only inside a nucleus

C
An isolated neutron can change into proton

D
An isolated proton can change into a neutron

Solution

$$\begin{array}{l}\text { The beta decay process within a nucleus can change a proton to a neutron. }\end{array}$$
Question 2
1 / -0

In a Bainbridge mass spectrometer positive rays of the same element produce different traces. The traces correspond to:

A
isotopes

B
isobars

C
isotones

D
none of the above

Solution

In a Bainbridge mass spectrometer positive rays of the same element produce different traces. The traces correspond to isotopes. Isotopes are atoms of same element. They have same atomic number (nuclear charge) but different mass number (number of neutrons). Positive rays (or anode rays or canal rays) contains ions obtained by knocking out electrons from gaseous atoms.
Question 3
1 / -0

When the radioactive isotope $$_{88}Ra^{226}$$ decays in a series by emission of three alpha$$(\alpha)$$ and a beta $$(\beta)$$ particle, the isotope X which remains undecay is?

A
$$_{83}X^{214}$$

B
$$_{84}X^{218}$$

C
$$_{84}X^{220}$$

D
$$_{87}X^{223}$$

Solution

Due to emission of $$3\alpha$$ particles, the mass number is reduced by $$12$$ while atomic number is decreased by $$6$$. Due to emission of $$\beta$$ particle, the atomic number is increased by one while there is no change in mass number. Now, resulting mass will be decreased by $$12$$ and atomic number is decreased by $$5$$. So, isotope X is $$_{83}X^{214}$$.
Question 4
1 / -0

Mass defect for the helium nucleus is $$0.0303\ amu$$. Binding energy per nucleon for this (in $$MeV$$) will be_______

A
$$28$$

B
$$7$$

C
$$4$$

D
$$1$$

Solution

Mass defect of helium nucleus $$\Delta M = 0.0303 \ amu$$
Binding energy $$E =\Delta Mc^2 = \Delta M\times 931.5 \ MeV$$
$$\implies \ E = 0.0303\times 931.5 = 28 \ MeV$$
Number of nucleon in helium nucleus $$=4$$
Thus binding energy per nucleon $$ = \dfrac{28}{4} =7 \ MeV$$
Question 5
1 / -0

Which of the following nucleus is fissionable by slow neutrons:

A
$$-{92}U^{238}$$

B
$$-{93}Np^{239}$$

C
$$-{92}U^{235}$$

D
$$_{2}I \, le^4$$

Solution

A
$$_{-92}U^{238}$$ is highly fissionable by slow neutrons.
Question 6
1 / -0

An unknown stable nuclide after absorbing a neutron emits an electron, and the new nuclide splits spontaneously into two alpha particles. The unknown nuclide can be

A
$$_4Be^9$$

B
$$_3Li^7$$

C
$$_2He^2$$

D
$$_5B^{10}$$

Solution

A neutron is a result of beta decay and as nucleus perform beta decay, it increases one proton. And the consequent two alpha decay also suggest that there are atleast 4 protons required. $${ _{ 3 }{ { Li }^{ 7 } } }$$ best suit the condition because 1 beta decay increases the proton to 4.
Ans: $${ _{ 3 }{ { Li }^{ 7 } } }$$
Question 7
1 / -0

A radioactive nucleus of mass $$M$$ emits a photon of frequency $$v$$ and the nucleus recoils. The recoil energy will be:

A
$$hv$$

B
$$M{ c }^{ 2 }-hv$$

C
$$\dfrac { { h }^{ 2 }{ v }^{ 2 } }{ 2M{ c }^{ 2 } } $$

D
$$Zero$$

Solution

Given,

Mass of nucleus $$=M$$

Frequency of photon $$=\upsilon $$

Velocity of nucleus $$={{V}_{2}}$$

Momentum of photon $$P=\dfrac{h}{\lambda }=\dfrac{h\nu }{c}$$

From conservation of momentum

Initial momentum = final momentum

$$ 0+0=M{{V}_{2}}+P $$

$$ {{V}_{2}}=\dfrac{P}{M}=\dfrac{h\nu }{Mc} $$

Recoil energy $$E=\dfrac{1}{2}M{{V}^{2}}=\dfrac{1}{2}M{{\left( \dfrac{h\nu }{Mc} \right)}^{2}}=\dfrac{{{h}^{2}}{{\nu }^{2}}}{2M{{c}^{2}}}$$
Recoil energy $$E=\dfrac{{{h}^{2}}{{\nu }^{2}}}{2M{{c}^{2}}}$$
Question 8
1 / -0

A $$\gamma$$ ray photon produces an electron positron pair. If the rest mass energy of electron is $$0.51\ Mev$$ and the total kinetic energy of electron - positron pair is $$0.78\ MeV$$ then the energy of $$\gamma$$- ray photon is $$Mev$$ is

A
$$0.78$$

B
$$1.8$$

C
$$1.28$$

D
$$0.28$$

Solution

Here total energy is that of the photon.
Positron has mass equal to the electron.
Hence its mass-energy also be equal.
Hence Total mass-energy is $$1.02Me_V$$
KE + this energy $$=$$photon energy.
$$1.02+0.78=1.8Me_V$$
Question 9
1 / -0

A nuclear transformation is denoted by $$X(n, \alpha)_{3}^{7}Li$$. Which of the following is the nucleus of element $$X$$?

A
$$_{6}^{12}C$$

B
$$_{5}^{10}B$$

C
$$_{5}^{9}B$$

D
$$_{4}^{11}Be$$

Solution

$$_{y}^{x}\textrm{X}$$ + $$_{0}^{1}\textrm{n}$$ $$\rightarrow$$ $$_{2}^{4}\textrm{He}$$ + $$_{3}^{7}\textrm{Li}$$

On balancing atomic number and mass number on both sides, we get
x=10 and y=5
so correct option is $$_{5}^{10}\textrm{B}$$
Question 10
1 / -0

Rn decays into Po by emitting an $$\alpha$$ particle with half life of 4 days. A sample contains $$6.4\ \times \ { 10 }^{ 10 }$$ atoms of Rn. After 12 days, the number of atoms of Rn left in the sample will be

A
$$3.2\ \times \ { 10 }^{ 10 }$$

B
$$0.53\ \times \ { 10 }^{ 10 }$$

C
$$2.1\ \times \ { 10 }^{ 10 }$$

D
$$0.8\ \times \ { 10 }^{ 10 }$$

Solution

$$\begin{array}{l}\text { Half Life }=t_{1 / 2}=4 \text { days } \\\text { Total time }=12 \text { days } \\T=n \times t_{1 / 2}, \quad n= \text {no. of half lives}\\\qquad \begin{array}{c}12=n \times 4 \\\text { }\end{array}\\n=3\end{array}$$

$$\begin{aligned}N &=N_{0} \times\left(\frac{1}{2}\right)^{n}..... \text { radioactivity equation }\\N_{0}&=6+4 \times 10^{10} ...\text { Given }\\N&=6.4\times10^{10}\left(\frac{1}{2}\right)^{3}\\&=\frac{6.4\times10^{10}}{8}\\&=0.8\times10^{10}\end{aligned}$$

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Nuclei Test - 45

Result

Nuclei Test - 45

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SHARING IS CARING

Question 1

A neutron can decay to a proton only inside a nucleus

A proton can change to a neutron only inside a nucleus

An isolated neutron can change into proton

An isolated proton can change into a neutron

Solution

Question 2

isotopes

isobars

isotones

none of the above

Solution

Question 3

$$_{83}X^{214}$$

$$_{84}X^{218}$$

$$_{84}X^{220}$$

$$_{87}X^{223}$$

Solution

Question 4

$$28$$

$$7$$

$$4$$

$$1$$

Solution

Question 5

$$-{92}U^{238}$$

$$-{93}Np^{239}$$

$$-{92}U^{235}$$

$$_{2}I \, le^4$$

Solution

Question 6

$$_4Be^9$$

$$_3Li^7$$

$$_2He^2$$

$$_5B^{10}$$

Solution

Question 7

$$hv$$

$$M{ c }^{ 2 }-hv$$

$$\dfrac { { h }^{ 2 }{ v }^{ 2 } }{ 2M{ c }^{ 2 } } $$

$$Zero$$

Solution

Question 8

$$0.78$$

$$1.8$$

$$1.28$$

$$0.28$$

Solution

Question 9

$$_{6}^{12}C$$

$$_{5}^{10}B$$

$$_{5}^{9}B$$

$$_{4}^{11}Be$$

Solution

Question 10

$$3.2\ \times \ { 10 }^{ 10 }$$

$$0.53\ \times \ { 10 }^{ 10 }$$

$$2.1\ \times \ { 10 }^{ 10 }$$

$$0.8\ \times \ { 10 }^{ 10 }$$

Solution

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