WBJEE 2025 Physics and Chemistry Papers

Let's analyze the decay chain step-by-step. We start with a nucleus X having atomic number Z and mass number A. The decay chain is as follows:
X

α

───▶

X1
In alpha decay, an alpha particle (helium nucleus) is emitted, which has a mass number of 4 and an atomic number of 2 .
Therefore:
X1: atomic number =Z−2,‌‌ mass number =A−4
X1

β

────▶

X2
In beta decay, a neutron is converted into a proton, increasing the atomic number by 1 while the mass number remains unchanged.
Therefore:
‌X2: atomic number =(Z−2)+1=Z−1, mass number =A−4
‌X2

α

────▶

X3
Again, alpha decay reduces the atomic number by 2 and the mass number by 4 .
Therefore:
X3: atomic number =(Z−1)−2=Z−3,‌‌ mass number =(A−4)−4=A−8
X3

γ

───▶

X4
Gamma decay does not change either the atomic number or the mass number.
Therefore:
X4: atomic number =Z−3, mass number =A−8
We are given that X4 has a mass number of 172 and an atomic number of 69 . This gives us two equations:
‌Z−3=69
‌A−8=172
Now, solve these equations:
From the first equation:
Z=69+3=72.
From the second equation:
A=172+8=180.
Thus, the original nucleus X has an atomic number of 72 and a mass number of 180 .