Download App

The Nucleus — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsThe Nucleus3 Marks
Question
A radioactive isotope is being produced at a constant rate $\frac{\text{dN}}{\text{dt}}=\text{R}$ in an experiment. The isotope has a half-life $\text{t}_{\frac{1}2{}}.$ Show that after a time $\text{t}>>\text{t}_{\frac{1}{2}},$ the number of active nuclei will become constant. Find the value of this constant.
✓

Answer

Given: Half life period $=\text{t}_{\frac{1}{2}}$ Rate of radio active decay $=\frac{\text{dN}}{\text{dt}}=\text{R}\Rightarrow\text{R}=\frac{\text{dN}}{\text{dt}}$ Given after time $\text{t}>>\text{t}_{\frac{1}{2}},$ the number of active nuclei will become constant. i.e. $\Big(\frac{\text{dN}}{\text{dt}}\Big)_{\text{present}}=\text{R}=\Big(\frac{\text{dN}}{\text{dt}}\Big)_{\text{decay}}$$\therefore\text{R}=\Big(\frac{\text{dn}}{\text{dt}}\Big)_{\text{decay}}$
$\Rightarrow\text{R}=\lambda\text{N}$ [where, $\lambda$ = Radioactive decay constant, N = constant number]
$\Rightarrow\text{R}=\frac{0.693}{\text{t}_{\frac{1}{2}}}(\text{N})\Rightarrow\text{Rt}_{\frac{1}{2}}=0.693\text{N}\Rightarrow\text{N}=\frac{\text{Rt}_{\frac{1}{2}}}{0.693}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from The Nucleus→The Nucleus — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Establish a relation between linear velocity and angular velocity in a uniform circular motion and explain the direction of linear velocity.
→
Define the instantaneous velocity and instantaneous acceleration and explain the difference.
→
A pole of length 1.00m stands half dipped in a swimming pool with water level 50.0 cm higher than the bed. The refractive index of water is 1.33 and sunlight is coming at an angle of 45° with the vertical. Find the length of the shadow of the pole on the bed.
→
If a body is taken to a height equal to the radius of earth from its surface, how much the weight of a body will decrease?
→
A force $\overrightarrow{\text{F}}=\overrightarrow{\text{v}}\times\overrightarrow{\text{A}}$ is exerted on a particle in addition to the force of gravity, where v is the velocity of the particle and $\overrightarrow{\text{A}}$ is a constant vector in the horizontal direction. With what minimum speed a particle of mass m be projected so that it continues to move undeflected with a constant velocity?
→
ls it always true that for two sources of equal intensity, the number of photons emitted in a given time are equal?
→
Two bodies of m and 4m are placed at a distance. The gravitational field is zero at a point on the line joining the two masses. What will be the gravitational potential at this point?
→
Find out whether these phenomena are reversible or not :
  1. Waterfall.
  2. Rusting of iron.
→
What should be the condition for the efficiency of a Carnot engine to be equal to 1?
→
A spring of constant k is attached with a mass m and is made to oscillate. What is its time period?
→