Question:
A radioactive element $^{242}_{92}X$ emits two $\alpha$ particles, one electron and two positrons. The product nucleus is represented by $^{234}_P Y$. The value of P is
A radioactive element $^{242}_{92}X$ emits two $\alpha$ particles, one electron and two positrons. The product nucleus is represented by $^{234}_P Y$. The value of P is
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$\alpha$ emission reduces Z by 2; $\beta^-$ (electron) increases Z by 1; $\beta^+$ (positron) reduces Z by 1.
Updated On: Apr 30, 2026
- 87
- 85
- 92
- 96
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The Correct Option is A
Solution and Explanation
Step 1: Analyze Particle Emissions
- 2 $\alpha$ ($^4_2He$): Total $Z$ change = $-4$, Total $A$ change = $-8$.
- 1 $\beta^-$ (electron $^0_{-1}e$): $Z$ change = $+1$.
- 2 $\beta^+$ (positron $^0_{+1}e$): $Z$ change = $-2$.
Step 2: Calculate Mass Number (A)
$A_{new} = 242 - 8 = 234$. (Matches question).
Step 3: Calculate Atomic Number (P)
$P = 92 (\text{Initial}) - 4 (\alpha) + 1 (\beta^-) - 2 (\beta^+)$
$P = 92 - 4 + 1 - 2 = 87$.
Step 4: Conclusion
The value of P is 87.
Final Answer:(A)
- 2 $\alpha$ ($^4_2He$): Total $Z$ change = $-4$, Total $A$ change = $-8$.
- 1 $\beta^-$ (electron $^0_{-1}e$): $Z$ change = $+1$.
- 2 $\beta^+$ (positron $^0_{+1}e$): $Z$ change = $-2$.
Step 2: Calculate Mass Number (A)
$A_{new} = 242 - 8 = 234$. (Matches question).
Step 3: Calculate Atomic Number (P)
$P = 92 (\text{Initial}) - 4 (\alpha) + 1 (\beta^-) - 2 (\beta^+)$
$P = 92 - 4 + 1 - 2 = 87$.
Step 4: Conclusion
The value of P is 87.
Final Answer:(A)
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