Question:
The distance of closest approach for an alpha nucleus of velocity $ v $ bombarding a stationary heavy nucleus target of charge $ Ze $ is directly proportional to
The distance of closest approach for an alpha nucleus of velocity $ v $ bombarding a stationary heavy nucleus target of charge $ Ze $ is directly proportional to
Updated On: Jun 2, 2024
- $ v $
- $ m $
- $ \frac{1}{v^{2}} $
- $ \frac{1}{Ze} $
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The Correct Option is C
Solution and Explanation
At the distance of closest approach $(d)$,
Kinetic energy of $\alpha$-particle
= Potential energy of $\alpha$- particle and target nucleus
$\therefore \frac{1}{2}mv^{2}=\frac{1}{4\pi\varepsilon_{0}} \frac{\left(2e\right)\left(ze\right)}{d}$
or $d=\frac{1}{4\pi\varepsilon_{0}} \frac{4Ze^{2}}{mv^{2}}$
$\therefore d \propto\frac{1}{v^{2}}$
Kinetic energy of $\alpha$-particle
= Potential energy of $\alpha$- particle and target nucleus
$\therefore \frac{1}{2}mv^{2}=\frac{1}{4\pi\varepsilon_{0}} \frac{\left(2e\right)\left(ze\right)}{d}$
or $d=\frac{1}{4\pi\varepsilon_{0}} \frac{4Ze^{2}}{mv^{2}}$
$\therefore d \propto\frac{1}{v^{2}}$
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Concepts Used:
Nuclear Physics
Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies the atom as a whole, including its electrons
Radius of Nucleus
‘R’ represents the radius of the nucleus. R = RoA1/3
Where,
- Ro is the proportionality constant
- A is the mass number of the element
Total Number of Protons and Neutrons in a Nucleus
The mass number (A), also known as the nucleon number, is the total number of neutrons and protons in a nucleus.
A = Z + N
Where, N is the neutron number, A is the mass number, Z is the proton number
Mass Defect
Mass defect is the difference between the sum of masses of the nucleons (neutrons + protons) constituting a nucleus and the rest mass of the nucleus and is given as:
Δm = Zmp + (A - Z) mn - M
Where Z = atomic number, A = mass number, mp = mass of 1 proton, mn = mass of 1 neutron and M = mass of nucleus.