A sample of radioactive nuclide `A^(150)` is having half life 2 hours and produce `B^(146)` after emitting `alpha` particle. Initially in sample only A was present having mass 50 gm. After four hours difference in mass of sample (A + B) is x gm then value of X is.

Answer

To solve the problem step by step, we will analyze the decay of the radioactive nuclide \( A^{150} \) and its transformation into \( B^{146} \) after emitting an alpha particle.

### Step 1: Understand the decay process
The radioactive nuclide \( A^{150} \) has a half-life of 2 hours. This means that after every 2 hours, half of the remaining \( A^{150} \) will decay into \( B^{146} \).

### Step 2: Determine the time period
We need to find the mass difference after 4 hours. Since the half-life is 2 hours, in 4 hours, there will be 2 half-lives.

### Step 3: Calculate the remaining mass of \( A^{150} \)
Initially, we have 50 grams of \( A^{150} \). After each half-life, the mass of \( A^{150} \) will be halved:
- After the first half-life (2 hours):
\[ \text{Remaining mass of } A = \frac{50 \text{ gm}}{2} = 25 \text{ gm} \]
- After the second half-life (4 hours):
\[ \text{Remaining mass of } A = \frac{25 \text{ gm}}{2} = 12.5 \text{ gm} \]

### Step 4: Calculate the mass of \( A^{150} \) that has decayed
The mass of \( A^{150} \) that has decayed after 4 hours is:
\[ \text{Mass of } A \text{ decayed} = \text{Initial mass} - \text{Remaining mass} = 50 \text{ gm} - 12.5 \text{ gm} = 37.5 \text{ gm} \]

### Step 5: Calculate the mass of \( B^{146} \) produced
When \( 150 \text{ gm} \) of \( A^{150} \) decays, it produces \( 146 \text{ gm} \) of \( B^{146} \). Therefore, the conversion ratio is:
\[ \frac{146 \text{ gm of } B}{150 \text{ gm of } A} \]
To find the mass of \( B^{146} \) produced from \( 37.5 \text{ gm} \) of \( A^{150} \):
\[ \text{Mass of } B = \frac{146}{150} \times 37.5 \text{ gm} = \frac{146 \times 37.5}{150} \]
Calculating this gives:
\[ \text{Mass of } B = \frac{5475}{150} = 36.5 \text{ gm} \]

### Step 6: Calculate the difference in mass between \( A^{150} \) and \( B^{146} \)
Now, we find the difference in mass between the remaining mass of \( A^{150} \) and the produced mass of \( B^{146} \):
\[ X = \text{Mass of } B - \text{Remaining mass of } A = 36.5 \text{ gm} - 12.5 \text{ gm} = 24 \text{ gm} \]

### Final Answer
Thus, the value of \( X \) is:
\[ \boxed{24 \text{ gm}} \]