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Physics Nuclei Atomic Masses and Composition of Nucleus

How does the number of neutrons affect the stability of a nucleus?

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Jaya Sharma

Contributor-Level 10

The number of neutrons in nucleus has an important role in determining the stability of nucleus. Stability of nucleus is affected by the balance between number of protons and neutrons and the number of nucleons. In lighter elements, the most stable nuclei has roughly equal number of protons and neutrons. For instance, Carbon-12 is the most common isotope of carbon with 6 protons and 6 neutrons.

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Physics Nuclei Atomic Masses and Composition of Nucleus

How does number of neutrons affect the stability of nucleus?

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Physics Nuclei Nuclei

Why do some elements have fractional atomic masses?

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Jaya Sharma

Contributor-Level 10

Most elements exist as a mixture of isotopes in nature. Isotopes are atoms of same elements that have same number of protons but they have different numbers of neutrons. Since the number of neutrons may vary, different isotopes of same element have different atomic masses.

The atomic mass of an element is a weighted average of atomic masses of its isotopes considering their natural abundances. The weighted average is calculated by multiplying atomic mass of every isotope by its natural abundance and then adding these products.

The atomic mass is an average that accounts for different masses and abundances of isotopes that results in a fr

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Physics Nuclei Class 12th

The half life period of radioactive element x is same as the mean life time of another radioactive element y. Initially they have the same number of atoms. Then:

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alok kumar singh

Contributor-Level 10

${(t_{\frac{1}{2}})}_{x} = {(t_{m e a n})}_{y}$
$\frac{l n 2}{λ_{x}} = \frac{1}{λ_{y}}$

$λ_{x} = (l n 2) λ_{y}$

Given N_x = N_y = N₀

So activity A = $λ N$

$A s λ_{x} < λ_{y} \Rightarrow A_{x} < A_{y}$

So y will decay faster than x.

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Physics Nuclei Class 12th

A sample of a radioactive nucleus A disintegrates to another radioactive nucleus B, which in turns disintegrates to some other stable nucleus C. Plot of a graph showing the variation of number of atoms of nucleus B vesus time is:

(Assume that a t = 0, there are no B atoms in the sample)

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Raj Pandey

Contributor-Level 9

$A \to_{}^{λ_{A}} B \to_{}^{λ_{B}} C$

Amount of B,

$N_{B} = \frac{λ_{A} N_{A_{0}}}{λ_{B} - λ_{A}} [e^{- λ_{A} t} - e^{- λ_{B} t}]$

where K = $\frac{λ_{A}}{λ_{B} - λ_{A}} N_{A_{0}}$

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Physics Nuclei Class 12th

There are 10¹⁰ radioactive nuclei in a given radioactive element, its half-time is 1 minute. How many nuclei will remain after 30 seconds?

$(\sqrt[]{2} = 1.414)$

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Vishal Baghel

Contributor-Level 10

$\frac{N}{N_{0}} = {(\frac{1}{2})}^{t |_{t_{1} | 2}}$

$\Rightarrow N = 1 0^{10} * {(\frac{1}{2})}^{\frac{1}{2}} = \frac{1 0^{10}}{\sqrt[]{2}} ? 7 * 1 0^{9}$

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Physics Nuclei Nuclei

At time t = 0, a material is composed of two radioactive atoms A and, B, where N_A(0) = 2N_B(0). The decay constant of both kind of radioactive atoms is $λ .$ However, A disintegrates to B and B disintegrates to C. Which of the following figures represents the evolution of N_B(t)/N_B(0) with respect to time t?

$[\begin{matrix} N_{A} (0) = N o . o f A a t o m s a t t = 0 & N_{B} (0) = N o . o f B a t o m s a t t = 0 \end{matrix}]$

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alok kumar singh

Contributor-Level 10

$\frac{d N_{B}}{d t} = λ N_{A} - λ N_{B} = 2 λ N_{B} (0) . e^{- λ t} - λ N_{B}$

$\Rightarrow \frac{d N_{B}}{d t} + λ N_{B} = 2 λ N_{B} (0) e^{- λ t}$

Solving it, $N_{B} (t) = N_{B} (0) (1 + 2 λ t) e^{- λ t}$

N_B (t) is maximum when,

$\frac{d N_{B}}{d t} = 0 \Rightarrow t = \frac{1}{2 λ}$

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Physics Nuclei Class 12th

Which of the following figure represents the variation of $I_{n} (\frac{R}{R_{0}})$ with I_nA (if R = radius of a nucleus and A = its mass number)

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alok kumar singh

Contributor-Level 10

We know, R = R_oA₃₌

_{$\Rightarrow \frac{R}{R_{O}} = A^{3}$}

Taking log both side

$l o g_{e} (\frac{R}{R_{O}}) = 3 l o g A$

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Physics Nuclei Class 12th

Read the following statements:

(A) Volume of the nucleus is directly proportional to the mass number.

(B) Volume of the nucleus is independent of mass number.

(C) Density of the nucleus is directly proportional to the mass number.

(D) Density of nucleus is directly proportional to the cube root of the mass number.

(E) Density of the nucleus is independent of the mass number.

Choose the correct option from the following options.

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Payal Gupta

Contributor-Level 10

Radius, R = R₀A^1/3

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