Question:

In the following nuclear reaction,
\(D \stackrel{α}{⟶} D1 \stackrel{β^-}{⟶} D2 \stackrel{α}{⟶} D3 \stackrel{γ}{⟶} D4\)
Mass number of D is 182 and atomic number is 74. Mass number and atomic number
of D4, respectively, will be _____.

Updated On: Sep 24, 2024
  • 174 and 71
  • 174 and 69
  • 172 and 69
  • 172 and 71
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The Correct Option is A

Solution and Explanation

The correct answer is (A) : 174 and 71
Equivalent reaction can be written as
D → D4 + 2α + β + γ
⇒ Mass number of D4 = Mass number of D – 2 × 4
= 182 – 8 = 174
⇒ Atomic number of D4
= Atomic number of D – 2 × 2 + 1
= 74 – 4 + 1 
= 71

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Concepts Used:

Nuclear Physics

Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies the atom as a whole, including its electrons

Radius of Nucleus

‘R’ represents the radius of the nucleus. R = RoA1/3

Where,

  • Ro is the proportionality constant
  • A is the mass number of the element

Total Number of Protons and Neutrons in a Nucleus

The mass number (A), also known as the nucleon number, is the total number of neutrons and protons in a nucleus.

A = Z + N

Where, N is the neutron number, A is the mass number, Z is the proton number

Mass Defect

Mass defect is the difference between the sum of masses of the nucleons (neutrons + protons) constituting a nucleus and the rest mass of the nucleus and is given as:

Δm = Zmp + (A - Z) mn - M

Where Z = atomic number, A = mass number, mp = mass of 1 proton, mn = mass of 1 neutron and M = mass of nucleus.