Question

An alpha particle (24He) has a mass of 4.00300 amu. A proton has a mass of 1.00783 amu and a neutron has a mass of 1.00867 amu respectively. The binding energy of alpha particles estimated from these data is the closest to.
(1) 20.4 MeV
(2) 32.0 MeV
(3) 24.3 MeV
(4) 27.9 MeV

Answer 1

Hint: Alpha particles, also known as alpha rays or alpha radiation, are made up of two protons and two neutrons bound together to form a helium-4 nucleus-like particle. They're usually made during the alpha decay process, but they can also be made in other ways. The net spin of alpha particles is zero and has a kinetic energy of about 5MeV. They are a form of particle radiation that is highly ionizing and has a shallow penetration depth (stopped by a few centimeters of air, or by the skin).

Complete step-by-step solution:
In this question, we have been given an alpha particle (24He), now for this particle we have few known quantities as
Number of protons = 2
Number of neutrons = 2
Mass of proton $m_p=1.00783$
Mass of Neutron $(m_n)=1.00867$
Now, we need to find the binding energy of the alpha particle.
Before finding the binding energy we will calculate the mass defect, it will make our further process easier.
Now, the mass defect can be given as
$\mathrm{\Delta }M=2m_p+2m_n-m_{He}$
Putting the values, we get
$\mathrm{\Delta }M=2\times (1.00783)+2\times (1.00867)-4.00300$
On solving this, we get
$\mathrm{\Delta }M=0.03$
Now, binding energy can be given as
$B.E.=\mathrm{\Delta }M\times 931.5\text{ MeV}$
Putting the values, we get
B.E. = 27.9 MeV
Hence, we can say that option (4) is the correct answer to this question.

Note: Alpha decay of heavier atoms is the most well-known cause of alpha particles. Due to the loss of four nucleons in the alpha particle, the mass number of an atom decreases by four as it releases an alpha particle in alpha decay. As a result of the loss of two protons, the atom's atomic number decreases by two, and the atom becomes a new element.