Test: Radioactivity - IIT JAM MCQ

Nuclei having n/p ratio close to 1 is more stable than the nuclei having n/p ratio greater or, less than 1.
Nuclei having n/p ratio greater than unity will undergo β-decay to increase n/p ratio 1. Similarly, nuclei n/p ratio less than 1 will undergo positron emission to increase n/p ratio to 1.
¹⁴C and ¹⁴O has n/p ratios (8/6) and (6/8) respectively.
Hence, ¹⁴C and ¹⁴O has n/p ratios greater and less than 1. Hence, they will undergo β-decay and positron emission.

Hence, the correct answer is : C.

Let the no. of α and β-particles are x and y respectively. According to Soddy-Fajan group displacement law when an alpha particle is released from an atom then the mass no. and atomic no. are decreased by four and two units respectively. Also, when an atom release a beta particle the mass no remains unchanged while the atomic no. is increased by one unit.

Hence, by this rule : 

So, 238 - 4x = 234 or, 4x = 4 or, x = 1 and 92 - 2x + y = 92 or, y = 92 - 92 + 2.1 = 2.

Hence, the no. of alpha and beta particles generated are: 1 and 2 respectively.
Hence, the correct answer is : A.

In boron neutron capture therapy, the following reaction takes place :

Hence, the initial boron isotope used and the particle generated after neutron capture respectively are : ₅B¹⁰ and α-particle.
Hence, the correct answer is: B.

When an alpha particle is emitted from an element, the mass no. and atomic no. of the parent element is decreased by four and two units respectively.

When a beta particle is emitted from an element, the mass no. of the daughter element remains same while atomic no. is increased by one unit.

Let the no. of alpha and beta particles are emitted by ₉₂U²³⁸ are x and y respectively. So, one write that _{92. 2x+y}U^238-4X correspond to ₈₂Pb²⁰⁶.

Hence, 238-4x = 206 or, 4x = 32 or, x = 8.
Also, 9 2 -2 x + y = 82 or, y = 82-92 + 1 6 = 6 .

Hence, the total no. of steps involved and no. of beta particles emitted in the spontaneous decay of ₉₂U²³⁸ → ₈₂Pb²⁰⁶ respectively, are (8 + 6) = 14 and 6 .
Hence, the correct answer is : B.

In case of the following equation, the total mass no. and proton no. of the species present on the left and right will be the same. An alpha particle has proton no. and mass no. equals to 2 and 4 respectively. Hence, the total mass no. of all the species on the left side o f the equation = (241 + 4 ) = 245 and the total proton no. of all the species present in the left = (95 + 2) = 97. Hence, the mass no. of X = (245 - 243) = 2 and the proton no. o f X = (97 - 97) = 0. Hence, X must be two neutron particles.
Hence, the correct answer is : A.

In the given process

The particle X has the atomic no. and mass no. 2 and 4 units respectively. This correspond to a α-particle.
Hence, the correct answer is : A.

The integrated rate equation for radioactivity is : kt = 2.303 log(N_o/N) or, 0.693t/t_1/2. 

Hence, the activity of the nuclide after 100 years would be 200 dis/min.
Hence, the correct answer is : C.

The radioactive isotope used to locate brain tumours is ₅₃I¹³¹.
Hence, the correct answer is : C.