Nuclei Easy Questions and Answers | Page - 19

Nuclei

The activity of a radioactive sample is measured as N₀ counts per minute at t = 0 and N₀ /e counts per minute at t = 5 minutes. The time (in minutes) at which the activity reduces to half its value is

1. log_e 2/5
1. 5/log_e 2
1. 5 log ₁₀2
1. 5 log_e 2

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N = N₀.e^{- λt}
Here, t = 5 minutes
N₀ = N₀.e^{- 5λ}
e

⇒ 5λ = 1,
λ = 1
5

Now, T_1/2 = ln2 = 5 ln2
λ

Correct Option: D

N = N₀.e^{- λt}
Here, t = 5 minutes
N₀ = N₀.e^{- 5λ}
e

⇒ 5λ = 1,
λ = 1
5

Now, T_1/2 = ln2 = 5 ln2
λ

The decay constant of a radio isotope is λ. If A₁ and A₂ are its activities at times t₁ and t₂ respectively, the number of nuclei which have decayed during the time (t₁ – t₂) :

1. λ (A₁ - A₂)
1. A₁t₁ - A₂t₂
1. A₁ - A₂
1. (A₁ - A₂)/λ

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Activity is given by
A = dN - λN
dt

A₁ = -λ N₁
and activity at time t₂ is A₂ = – l N₂ As t₁ > t₂ , therefore, number of atoms remained after time t₁ is less than that remained after time t₂ . That is, N₁ < N₂ .
∴ number of nuclei decayed in (t₁ – t₂)
= N₂ - N₁ = (A₁ - A₂)
λ

Correct Option: D

Activity is given by
A = dN - λN
dt

A₁ = -λ N₁
and activity at time t₂ is A₂ = – l N₂ As t₁ > t₂ , therefore, number of atoms remained after time t₁ is less than that remained after time t₂ . That is, N₁ < N₂ .
∴ number of nuclei decayed in (t₁ – t₂)
= N₂ - N₁ = (A₁ - A₂)
λ

The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an

1. isomer of parent
1. isotone of parent
1. isotope of parent
1. isobar of parent

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Isotopes of an element have the same atomic number but different mass number. A radioactive substance when emits one alpha particles ⁴_{2He , its mass number reduces by 4 and charge no.reduces by 2 and after emission of two β-particles its charge no. increase by 2 thus the charge no. i.e. atomic number remains the same.}

Correct Option: C

Isotopes of an element have the same atomic number but different mass number. A radioactive substance when emits one alpha particles ⁴_{2He , its mass number reduces by 4 and charge no.reduces by 2 and after emission of two β-particles its charge no. increase by 2 thus the charge no. i.e. atomic number remains the same.}

In a radioactive decay process, the negatively charged emitted β-particles are

1. the electrons produced as a result of the decay of neutrons inside the nucleus
1. the electrons produced as a result of collisions between atoms
1. the electrons orbiting around the nucleus
1. the electrons present inside the nucleus

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In beta minus decay (β–), a neutron is transformed into a proton, and an electron is emitted from the nucleus along with antineutrino.
n = p + e^- + V

Correct Option: A

In beta minus decay (β–), a neutron is transformed into a proton, and an electron is emitted from the nucleus along with antineutrino.
n = p + e^- + V

The half life of radium is about 1600 years. Of 100 g of radium existing now, 25 g will remain unchanged after

1. 3200 years
1. 4800 years
1. 6400 years
1. 2400 years

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100 g will become 25 g in two half lives, so, it is 3200 years.

Correct Option: A

100 g will become 25 g in two half lives, so, it is 3200 years.