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Not only particles such as electrons and protons but also entire atoms can be classified as fermions or bosons, depending on whether their overall spin quantum numbers are, respectively, half-integral or integral. Consider the helium isotopes He3and He4. Which of the following statements is correct? (a) Both are fermions. (b) Both are bosons. (c)He4is a fermion, and He3is a boson. (d)He3is a fermion, and He4is a boson. (The two helium electrons form a closed shell and play no role in thisdetermination.)

Short Answer

Expert verified

(a) Not correct

(b) Not correct

(c) Not correct

(d) Correct

Step by step solution

01

Identifying the data given in the question

He3and He4are two isotopes of helium.

02

Concept used to solve the question

Fermion

Any particle with an odd half-integer spin, such as 1/2 , 3/2 and so on, is referred to as a fermion.

Bosons

Bosons are particles with integer spins 0,1,2.

03

Step 3(a) : Checking statement (a)

Fermions have a half-integer spin and bosons have an integer spin.

He4has two protons and two neutrons.

In localid="1663128163011" He4 total spin is zero since its neutron and proton spins are positioned in opposition to one another Therefore it is a boson.

He3has two protons and one neutron The proton spins in He3are oppositely aligned so they have total spin 0, whereas the last neutron has spin 1/2. He3has a 1/2 spin as a result it is a fermion.

Since both are not fermions therefore this statement is not true.

04

Step 4(b) : Checking statement (b) 

Fermions have a half-integer spin, whereas bosons have an integer spin.

He4has two protons and two neutrons.

He4has total spin is zero since its neutron and proton spins are positioned in opposition to one another. Therefore it is a boson.

He3has two protons and one neutron The proton spins in He3are oppositely aligned (total spin 0 ), whereas the last neutron has spin 1/2 . He3has a spin 1/2 as a result it is a fermion.

Since both are not boson therefore this statement is not true.

05

Step 5(c) : Checking statement (c) 

Fermions have a half-integer spin and bosons have an integer spin.

He4has two protons and two neutrons.

He4has total spin zero since its neutron and proton spins are positioned in opposition to one another Therefore it is a boson.

He3has two protons and one neutron The proton spins in He3are oppositely aligned (total spin 0), whereas the last neutron has spin 1/2 . He3has a 1/2 spin as a result it is a fermion.

Since He3not is a boson and He4is not a fermion therefore this statement is not true.

06

Step 6(d) : Checking statement (d) 

Fermions have a half-integer spin and bosons have an integer spin.

He4has two protons and two neutrons.

He4has total spin zero since its neutron and proton spins are positioned in opposition to one another Therefore it is a boson.

He3has two protons and one neutron The proton spins in He3are oppositely aligned (total spin 0 ), whereas the last neutron has spin 1/2 . He3has a 1/2 spin as a result it is a fermion.

Since is a fermion and He4is a boson therefore this statement is true

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