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A radioactive nucleus (initial mass number A and atomic number

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A radioactive nucleus (initial mass number $A$ and atomic number $Z$ ) emits $3 α$ -particles and 2 positrons. The ratio of number of neutrons to that of protons in the final nucleus will be
(a) $\frac{A - Z - 8}{Z - 4}$
(b) $\frac{A - Z - 4}{Z - 8}$
(c) $\frac{A - Z - 12}{Z - 4}$
(d) $\frac{A - Z - 4}{Z - 2}$

Views: 5,997 students

Updated on: Nov 6, 2023

Book:

Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2010

Found 2 tutors discussing this question

Evelyn Discussed

A radioactive nucleus (initial mass number

A

and atomic number

Z

) emits

3 α

-particles and 2 positrons. The ratio of number of neutrons to that of protons in the final nucleus will be
(a)

\frac{A - Z - 8}{Z - 4}

(b)

\frac{A - Z - 4}{Z - 8}

(c)

\frac{A - Z - 12}{Z - 4}

(d)

\frac{A - Z - 4}{Z - 2}

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

Exp. (b)
In positive beta decay, a proton is transformed into a neutron and a positron is emitted.

p^{+} ⟶ n^{0} + e^{+}

Number of neutrons initially was

A - Z

.
Number of neutrons after decay

(A - Z) - 3 \times 2

(due to alpha particles)

+ 2 \times 1

(due to positive beta decay)
The number of protons will reduce by 8 .
[as

3 \times 2

(due to alpha particles)

+ 2

(due to
positive beta decay)]
Hence, atomic number reduces by 8 .
So, the ratio of number of neutrons to that of protons

= \frac{A - Z - 4}{Z - 8}

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Question Text	A radioactive nucleus (initial mass number $A$ and atomic number $Z$ ) emits $3 α$ -particles and 2 positrons. The ratio of number of neutrons to that of protons in the final nucleus will be (a) $\frac{A - Z - 8}{Z - 4}$ (b) $\frac{A - Z - 4}{Z - 8}$ (c) $\frac{A - Z - 12}{Z - 4}$ (d) $\frac{A - Z - 4}{Z - 2}$
Updated On	Nov 6, 2023
Topic	Nuclei
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 3
Upvotes	355
Avg. Video Duration	6 min

Text solutionVerified

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A radioactive nucleus (initial mass number A and atomic number Z ) emits 3α-particles and 2 positrons. The ratio of number of neutrons to that of protons in the final nucleus will be(a) Z−4A−Z−8​(b) Z−8A−Z−4​(c) Z−4A−Z−12​(d) Z−2A−Z−4​

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Questions from JEE Mains 2010 - PYQs

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