Physics Q27 – NEET-UG 2024

_{82}^{290} X \overset{α}{\to} Y \overset{e^{+}}{\to} Z \overset{β^{-}}{\to} P \overset{e^{-}}{\to} Q

In the nuclear emission stated above, the mass number and atomic number of the product

Q

respectively, are :

Clue 1 of 3: Nuclear Decay Types

Understand the changes in mass number and atomic number for different types of nuclear decay.

🧠 Full Solution Path

Step 1: Analyze Initial Nucleus and Decay Chain✦ Active

The initial nucleus is $_{82}^{290} X$ . This means its mass number ( $A$ ) is $290$ and its atomic number ( $Z$ ) is $82$ . The decay chain involves four sequential steps: an $α$ -decay, a positron ( $e^{+}$ ) emission, a $β^{-}$ emission, and another $e^{-}$ emission.

Step 2: Apply Decay Rules Sequentially○ Expand

Let's track the mass number ( $A$ ) and atomic number ( $Z$ ) through each decay step:

1. ** $α$ -decay ( $X \to Y$ ):** An $α$ -particle is a helium nucleus ( $_{2}^{4} H e$ ). Mass number ( $A$ ) decreases by 4: $A_{Y} = 290 - 4 = 286$ . Atomic number ( $Z$ ) decreases by 2: $Z_{Y} = 82 - 2 = 80$ . So, $Y$ is $_{80}^{286} Y$ .

2. ** $e^{+}$ -emission ( $Y \to Z$ ):** A positron ( $e^{+}$ or $_{+ 1}^{0} e$ ) emission occurs when a proton converts to a neutron. Mass number ( $A$ ) remains unchanged: $A_{Z} = 286$ . Atomic number ( $Z$ ) decreases by 1: $Z_{Z} = 80 - 1 = 79$ . So, $Z$ is $_{79}^{286} Z$ .

3. ** $β^{-}$ -emission ( $Z \to P$ ):** A beta-minus particle ( $e^{-}$ or $_{- 1}^{0} e$ ) emission occurs when a neutron converts to a proton. Mass number ( $A$ ) remains unchanged: $A_{P} = 286$ . Atomic number ( $Z$ ) increases by 1: $Z_{P} = 79 + 1 = 80$ . So, $P$ is $_{80}^{286} P$ .

4. ** $e^{-}$ -emission ( $P \to Q$ ):** This is another beta-minus particle ( $e^{-}$ or $_{- 1}^{0} e$ ) emission. Mass number ( $A$ ) remains unchanged: $A_{Q} = 286$ . Atomic number ( $Z$ ) increases by 1: $Z_{Q} = 80 + 1 = 81$ . So, $Q$ is $_{81}^{286} Q$ .

💡 Teacher's Secret Hint

Remember that $e^{+}$ emission is also known as positron emission, and $e^{-}$ emission is also known as $β^{-}$ decay.

Step 3: State Final Mass and Atomic Numbers○ Expand

The final product $Q$ has a mass number of $286$ and an atomic number of $81$ . This corresponds to option (3).

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Physics Question 27 – NEET-UG 2024

Clue 1 of 3: Nuclear Decay Types

🧠 Full Solution Path