
In an decay, the kinetic energy of particles is and value of the reaction is . The mass number of the mother nucleus is . Find the value of . (Assume that daughter nucleus is in the ground state)
A)
B)
C)
D)
Answer
134.4k+ views
Hint: Before proceeding with our solution, let us discuss the various terms we will use. Alpha decay is a radioactive decay in which a nucleus emits an alpha particle (which is nothing but an ionised helium nucleus) and thereby transforms into a different atomic nucleus, with a mass number that is reduced by four and an atomic number that is reduced by two. The Q value for a reaction is the amount of energy absorbed or released during the nuclear reaction and can be determined from the masses of reactants and products. Q values affect reaction rates.
Formula Used:
Complete step by step solution:
As we know that alpha decay causes changes in the atomic number and mass number of the mother nucleus, mathematically shown as
where is the mother nucleus, is the daughter nucleus, is the alpha particle and the subscripts denote the atomic numbers of the respective nuclei and the superscripts denote the mass number of the respective nuclei.
We know the relation between the kinetic energy of the alpha particle and the total energy of the reaction is given as
where is the kinetic energy of the alpha particle, is the total energy change of the reaction, is the mass of the daughter nucleus and is the mass of the alpha particle.
We have been given that kinetic energy of the alpha particle
Total energy change in the reaction
From the reaction of the alpha decay of a mother nucleus given above, we can say that
Mass of the daughter nucleus
We know that mass of an alpha particle
Substituting the values given to us, we get
Cross multiplying, we get
But we have to find the value of which will be
Hence option (B) is the correct answer.
Note: We were not provided with the mass of the daughter nucleus; we had to find it using the mass of the mother nucleus and the mass of an alpha particle. Also, keep in mind that we were asked the value of the mass of the mother nucleus divided by four and not the mass itself. Students almost always choose the wrong option in such cases, even after getting the right answer.
Formula Used:
Complete step by step solution:
As we know that alpha decay causes changes in the atomic number and mass number of the mother nucleus, mathematically shown as
We know the relation between the kinetic energy of the alpha particle and the total energy of the reaction is given as
We have been given that kinetic energy of the alpha particle
Total energy change in the reaction
From the reaction of the alpha decay of a mother nucleus given above, we can say that
Mass of the daughter nucleus
We know that mass of an alpha particle
Substituting the values given to us, we get
Cross multiplying, we get
But we have to find the value of
Hence option (B) is the correct answer.
Note: We were not provided with the mass of the daughter nucleus; we had to find it using the mass of the mother nucleus and the mass of an alpha particle. Also, keep in mind that we were asked the value of the mass of the mother nucleus divided by four and not the mass itself. Students almost always choose the wrong option in such cases, even after getting the right answer.
Recently Updated Pages
JEE Main 2025 Session 2 Form Correction (Closed) – What Can Be Edited

What are examples of Chemical Properties class 10 chemistry JEE_Main

JEE Main 2025 Session 2 Schedule Released – Check Important Details Here!

JEE Main 2025 Session 2 Admit Card – Release Date & Direct Download Link

JEE Main 2025 Session 2 Registration (Closed) - Link, Last Date & Fees

JEE Mains Result 2025 NTA NIC – Check Your Score Now!

Trending doubts
JEE Main 2025: Conversion of Galvanometer Into Ammeter And Voltmeter in Physics

Wheatstone Bridge for JEE Main Physics 2025

Elastic Collisions in One Dimension - JEE Important Topic

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

Free Radical Substitution Mechanism of Alkanes for JEE Main 2025

AB is a long wire carrying a current I1 and PQRS is class 12 physics JEE_Main

Other Pages
Diffraction of Light - Young’s Single Slit Experiment

Write the value of charge in coulombs on the nucleus class 12 physics JEE_Main

CBSE Class 12 English Core Syllabus 2024-25 - Revised PDF Download

CBSE Date Sheet 2025 Class 12 - Download Timetable PDF for FREE Now

JEE Main 2025 Session 2: Exam Date, Admit Card, Syllabus, & More

CBSE Class 10 Hindi Sample Papers with Solutions 2024-25 FREE PDF
