A count rate meter shows a count of $240$ per minute from a given radioactive source. One hour later the meter shows a count rate of $30$ per minute. The half-life of the source is?

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Answer 1

The number of counts left after time t
$N = N_{0} (\frac{1}{2})^{t / T_{1 / 2}}$
$∴ 30 = 240 (\frac{1}{2})^{60 / T_{1 / 2}}$
$[∵ t = 1 h = 60 m i n]$
or $\frac{3 0}{2 4 0} = (\frac{1}{2})^{60 / T_{1 / 2}}$
or $(\frac{1}{2})^{3} = (\frac{1}{2})^{60 / T_{1 / 2}}$
Comparing the powers, we get
$∴ \frac{6 0}{T _{1 / 2}} = 3$
$T_{1 / 2} = \frac{6 0}{3}$
or $T_{1 / 2} = 20$ min.

Answer 2

The number of counts left after time t

N = N_{0} (\frac{1}{2})^{t / T_{1 / 2}}

∴ 30 = 240 (\frac{1}{2})^{60 / T_{1 / 2}}

[∵ t = 1 h = 60 m i n]

or

\frac{3 0}{2 4 0} = (\frac{1}{2})^{60 / T_{1 / 2}}

or

(\frac{1}{2})^{3} = (\frac{1}{2})^{60 / T_{1 / 2}}

Comparing the powers, we get

∴ \frac{6 0}{T _{1 / 2}} = 3

T_{1 / 2} = \frac{6 0}{3}

or

T_{1 / 2} = 20

min.

A count rate meter shows a count of $240$ per minute from a given radioactive source. One hour later the meter shows a count rate of $30$ per minute. The half-life of the source is?

$80$ min

$120$ min

$20$ min

$30$ min

A rate-meter measures the number of disintegrations per second from a radioactive source. It gives a count of $320$ counts per second. Ninety minutes later, it gives $40$ counts per second. The half life of the source is

A piece of bone from an archaeological site is found to give a count rate of $15$ counts per minute. A similar sample of fresh bone gives a count rate of $19$ counts per minute. Calculate the age of the specimen. Given $T_{1 / 2} = 5570 y e a r s$

A freshly made radioactive sample gives a count rate of $8000$ counts per minute. After twenty days, it gives a count-rate of $500$ counts per minute. What is the half-life of the material?

Answer the question:
A radioactive source produces a count rate on a detector of $1600$ counts / s. After $32$ hours the count rate has fallen to $100$ counts/s.
Both count rates have been corrected for background radiation.
What is the half-life of the source ?

The activity of a radioactive sample is measured as $N_{0}$ counts per minute at $t = 0$ and $N_{0} / e$ counts per minute at $t = 5$ min. The time, (in minute) at which the activity reduces to half its value, is :

Revise with Concepts

Discovery of Radiation

Introduction to Radioactivity

Alpha, Beta and Gamma Emission

Differentiate Between Alpha, Beta and Gamma Radiations

Background Radiations

A count rate meter shows a count of 240 per minute from a given radioactive source. One hour later the meter shows a count rate of 30 per minute. The half-life of the source is?

80min

120min

20min

30min

The number of counts left after time t N=N0​(21​)t/T1/2​ ∴30=240(21​)60/T1/2​ [∵t=1h=60min] or 24030​=(21​)60/T1/2​ or (21​)3=(21​)60/T1/2​ Comparing the powers, we get ∴T1/2​60​=3 T1/2​=360​ or T1/2​=20min.

A rate-meter measures the number of disintegrations per second from a radioactive source. It gives a count of 320 counts per second. Ninety minutes later, it gives 40 counts per second. The half life of the source is

A piece of bone from an archaeological site is found to give a count rate of 15 counts per minute. A similar sample of fresh bone gives a count rate of 19 counts per minute. Calculate the age of the specimen. Given T1/2​=5570 years

A freshly made radioactive sample gives a count rate of 8000 counts per minute. After twenty days, it gives a count-rate of 500 counts per minute. What is the half-life of the material?

Answer the question: A radioactive source produces a count rate on a detector of 1600 counts / s. After 32 hours the count rate has fallen to 100 counts/s. Both count rates have been corrected for background radiation. What is the half-life of the source ?

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 min. The time, (in minute) at which the activity reduces to half its value, is :

Revise with Concepts

Discovery of Radiation

Introduction to Radioactivity

Alpha, Beta and Gamma Emission

Differentiate Between Alpha, Beta and Gamma Radiations

Background Radiations

A count rate meter shows a count of $240$ per minute from a given radioactive source. One hour later the meter shows a count rate of $30$ per minute. The half-life of the source is?

$80$ min

$120$ min

$20$ min

$30$ min

A rate-meter measures the number of disintegrations per second from a radioactive source. It gives a count of $320$ counts per second. Ninety minutes later, it gives $40$ counts per second. The half life of the source is

A piece of bone from an archaeological site is found to give a count rate of $15$ counts per minute. A similar sample of fresh bone gives a count rate of $19$ counts per minute. Calculate the age of the specimen. Given $T_{1 / 2} = 5570 y e a r s$

A freshly made radioactive sample gives a count rate of $8000$ counts per minute. After twenty days, it gives a count-rate of $500$ counts per minute. What is the half-life of the material?

Answer the question:
A radioactive source produces a count rate on a detector of $1600$ counts / s. After $32$ hours the count rate has fallen to $100$ counts/s.
Both count rates have been corrected for background radiation.
What is the half-life of the source ?

The activity of a radioactive sample is measured as $N_{0}$ counts per minute at $t = 0$ and $N_{0} / e$ counts per minute at $t = 5$ min. The time, (in minute) at which the activity reduces to half its value, is :