You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Law of Radioactivity

To determine ...

Question

To determine the half life of a radioactive element, a student plots a graph of $l n | \frac{d N (t)}{d t} |$ versus $t$ . Here $\frac{d N (t)}{d t}$ is the rate of radioactive decay at time $t$ . If the number of radioactive nuclei of this element decreases by a factor ofp after 4.16 years, the value of $p$ is:

8

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

9

No worries! We‘ve got your back. Try BYJU‘S free classes today!

10

No worries! We‘ve got your back. Try BYJU‘S free classes today!

11

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D $8$
$N = N_{0} e^{- λ t}$

$l n | \frac{d N}{d t} | = l n (N_{0} λ) - λ t$
From graph, $λ = \frac{1}{2}$ per year
$t_{1 / 2} = \frac{0.693}{1 / 2} = 1.386$ year
$4.16 y r s = 3 t_{1 / 2}$
$∴ p = 8$

Suggest Corrections

Similar questions

Q. To determine the half life of a radioactive element, student plots a graph of

l n | d N (t) / d t |

versus

t

. Here

d N (t) / d t

is the rate of radioactive decay at time

t .

If the number of radioactive nuclei of this element decreases by a factor of

p

after

4.16

years, the value of

p

is ......

Q. To determine the half life of a radioactive element, student plots a graph of

ln ∣ ∣ ∣ \frac{d N (t)}{d t} ∣ ∣ ∣

versus

t

. Here

d N (t) / d t

is the rate of radioactive decay at time

t

. If the number of radioactive nuclei of this element decreases by a factor of

p

after

4.16 years

, the value of

p

is ____. (Round off the nearest integer)

(e^{4.16} = 64.07)

Q. To determine the half life of a radioactive element a student plots a graph of

l n ∣ ∣ ∣ \frac{d N (t)}{d t} ∣ ∣ ∣

versus

t

. Here

\frac{d N (t)}{d t}

is the rate of radio active decay at time

t

. If the number of radio active nuclei of this element decreases by a factor of

p

after

4.16 y e a r s

, the value

p

is:

Q. A radioactive isotope is being produced at a constant rate

A

. The isotope has a half-life

T

. Initially, there are no decayed nuclei. After a time

t (t >>> T)

, the number of decayed nuclei becomes constant. The value of this constant is,

Q. Nuclei of radioactive element A are produced at rate '

t^{2}

' at any time t. The element A has decay constant

λ

. Let N be the number of nuclei of element A at any time t. At time

t = t_{0}, \frac{d N}{d t}

is minimum. N is :

Join BYJU'S Learning Program

To determine the half life of a radioactive element, a student plots a graph of ln|dN(t)dt| versus t. Here dN(t)dt is the rate of radioactive decay at time t. If the number of radioactive nuclei of this element decreases by a factor ofp after 4.16 years, the value of p is:

The correct option is D 8N=N0e−λtln|dNdt|=ln(N0λ)−λtFrom graph, λ=12 per year t1/2=0.6931/2=1.386 year4.16yrs=3t1/2∴p=8

The correct option is D $8$
$N = N_{0} e^{- λ t}$

$l n | \frac{d N}{d t} | = l n (N_{0} λ) - λ t$
From graph, $λ = \frac{1}{2}$ per year
$t_{1 / 2} = \frac{0.693}{1 / 2} = 1.386$ year
$4.16 y r s = 3 t_{1 / 2}$
$∴ p = 8$