
According to Einstein’s theory of relativity, mass can be converted into energy and vice-versa. The lightest elementary particle, taken to be the electron, has a mass equivalent to of energy. Which of the following statements are true?
A) The minimum amount of energy available through the conversion of mass into energy is .
B) The least energy of a - photon that can be converted into mass is .
C) The minimum energy released by the conversion of mass into energy is , it is a - photon of energy and energy above that can be converted into mass.
D) The minimum energy released by the conversion of mass into energy is , it is a - photon of energy and energy above that can be converted into mass.
Answer
494.1k+ views
Hint:The conversion of the mass of the electron into energy refers to the annihilation of an electron-positron pair. The annihilation of the pair generates a - photon whose least energy equals the sum of the rest mass energies of the electron and the positron.
Complete step by step answer:
Step 1: Express the reaction involved in the conversion of the mass of the electron into energy.
Here, it is mentioned that the mass of the electron is converted into energy. This refers to the annihilation of the electron-positron pair. The reaction produces a - photon. The annihilation can be represented as .
The rest mass-energy of the electron is given to be . The positron has the same rest mass-energy. So, the minimum energy produced by the above reaction is .
The first statement is in correspondence with the obtained minimum energy.
The fourth statement mentions the minimum energy produced in the conversion to be .
Thus the first statement is correct but the fourth statement is not.
Step 2: Give the least energy of the - photon to see if the second and third statements hold.
The minimum energy produced by the conversion serves as the least energy of the - photon. Thus the least energy of the - photon will be .
The second statement is in correspondence with the obtained least energy of the photon.
The third statement suggests that out of the minimum energy produced in the conversion, will be the energy of the - photon and the rest can be converted into mass.
So, the second statement is true but the third statement is false.
Therefore, the correct options are A and B.
Note:In the annihilation of an electron-positron pair to produce a - photon, it is the total mass of the particles and not a part of it that gets converted into energy. Similarly, in the production of an electron-positron pair by a - photon, it is the total energy of the photon that gets converted into mass. In the reaction, the charge is conserved as the electron has a charge , the positron has a charge and the - photon has no charge.
Complete step by step answer:
Step 1: Express the reaction involved in the conversion of the mass of the electron into energy.
Here, it is mentioned that the mass of the electron is converted into energy. This refers to the annihilation of the electron-positron pair. The reaction produces a
The rest mass-energy of the electron is given to be
The first statement is in correspondence with the obtained minimum energy.
The fourth statement mentions the minimum energy produced in the conversion to be
Thus the first statement is correct but the fourth statement is not.
Step 2: Give the least energy of the
The minimum energy produced by the conversion serves as the least energy of the
The second statement is in correspondence with the obtained least energy of the photon.
The third statement suggests that out of the minimum energy produced in the conversion,
So, the second statement is true but the third statement is false.
Therefore, the correct options are A and B.
Note:In the annihilation of an electron-positron pair to produce a
Recently Updated Pages
Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Master Class 12 Social Science: Engaging Questions & Answers for Success

Master Class 12 Chemistry: Engaging Questions & Answers for Success

Class 12 Question and Answer - Your Ultimate Solutions Guide

Master Class 11 Business Studies: Engaging Questions & Answers for Success

Trending doubts
Draw a labelled sketch of the human eye class 12 physics CBSE

a Tabulate the differences in the characteristics of class 12 chemistry CBSE

Which one of the following is a true fish A Jellyfish class 12 biology CBSE

Why is the cell called the structural and functional class 12 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Write the difference between solid liquid and gas class 12 chemistry CBSE
