Question
The count rate from a radioactive sample falls from 4.0 × 106 per second to 1.0 × 106 per second in 20 hours. What will be the count rate 100 hours after the beginning?
✓
Answer
$\text{A}_0=4\times10^5$ disintegration/sec
$\text{A}'=1\times10^6$
dis/sec; t = 20 hours.$\text{A}'=\frac{\text{A}_0}{2^{\frac{\text{t}}{\text{t}_{\frac{1}{2}}}}}\Rightarrow2^{\frac{\text{t}}{\text{t}_{\frac{1}{2}}}}=\frac{\text{A}_0}{\text{A}'}\Rightarrow2^{\frac{\text{t}}{\text{t}_{\frac{1}{2}}}}=4$
$\Rightarrow\frac{\text{t}}{\text{t}_{\frac{1}{2}}}=2\Rightarrow\text{t}^{\frac{1}{2}}=\frac{\text{t}}{2}=\frac{20\text{ hours}}{2}=10\text{ hours}.$
$\text{A}''=\frac{\text{A}_0}{2^{\frac{\text{t}}{\text{t}_{\frac{1}{2}}}}}\Rightarrow\text{A}''=\frac{4\times10^6}{2^{\frac{100}{10}}}$
$=0.00390625\times10^6=3.9\times10^3$
dintegrations/sec.Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A totally reflecting, small plane mirror placed horizontally faces a parallel beam of light, as shown in the figure. The mass of the mirror is 20g. Assume that there is no absorption in the lens and that 30% of the light emitted by the source goes through the lens. Find the power of the source needed to support the weight of the mirror. Take g = 10m/s2.
Consider a sample of oxygen at 300K. Find the average time taken by a molecule to travel a distance equal to the diameter of the earth.
The pendulum of a certain clock has time period 2.04s. How fast or slow does the clock run during 24 hours?
A convex lens of focal length 20 cm is placed coaxially with a convex mirror of radius of curvature 20 cm. The two are kept 15 cm apart. A point object is placed 40 cm in front of the convex lens. Find the position of the image formed by this combination. Draw the ray diagram showing the image formation.
A spherical volume contains a uniformly distributed charge of density 2.0 × 10-4Cm-3. Find the electric field at a point inside the volume at a distance 4.0cm from the centre.
Light of frequency 7.21 × 1014 Hz is incident on a metal surface. Electrons with a maximum speed of 6.0 × 105 m/s are ejected from the surface. What is the threshold frequency for photoemission of electrons?
Define the term ‘decay constant’ of a radioactive sample. The rate of disintegration of a given radioactive nucleus is 10000 disintegrations/ s and 5,000 disintegrations/ s after 20hr. and 30hr. respectively from start. Calculate the half life and initial number of nuclei at t = 0.
A monochromatic light source of intensity 6mW emits 8 × 1016 photons per second. This light ejects photoelectrons from a metal surface. The stopping potential for this setup is 2.0V. Calculate the work function of the metal.
A light ray falling at an angle of 45° with the surface of a clean slab of ice of thickness 1m is refracted into it at an angle of 30°. Calculate the time taken by the light rays, to cross the slab. Speed of light in vacuum = 3 × 108m/s
For the potentiometer circuit shown in the given figure, points X and Y reprensent the two terminals of an unknown emf E'. A student observed that when the jockey in moved from the end A to the end B of the potentiometer wire, the deflection in the galvanometer remains in the same direction.
What may be the two possible faults in the circuit that could result in this obsevation?
If the galvanometer deflection at the end B is (i) more, (ii) less, than that at the end A, which of the two faults, listed above, would be there in the circuit?
Give reasons in support of your answer in each case.
What may be the two possible faults in the circuit that could result in this obsevation?If the galvanometer deflection at the end B is (i) more, (ii) less, than that at the end A, which of the two faults, listed above, would be there in the circuit?
Give reasons in support of your answer in each case.