Download App

Nuclei — Physics STD 12 Science — Question

Bihar BoardEnglish MediumSTD 12 SciencePhysicsNuclei5 Marks
Question
A point source emitting alpha particles is placed at a distance of 1m from a counter which records any alpha particle falling on its 1cm2 window. If the source contains 6.0 × 1016 active nuclei and the counter records a rate of 50000 counts/ second, find the decay constant. Assume that the source emits alpha particles uniformly in all directions and the alpha particles fall nearly normally on the window.
✓

Answer

Counts received per cm2 = 50000 Counts/sec.
N = N3o of active nucleic = 6 × 1016
Total counts radiated from the source = Total surface area × 50000 counts/cm2
= 4 × 3.14 × 1 × 104 × 5 × 104 = 6.28 × 109 $\text{Counts}=\frac{\text{dN}}{\text{dt}}$
We know, $\frac{\text{dN}}{\text{dt}}=\lambda\text{N}$
$\lambda=\frac{6.28\times10^9}{6\times10^{16}}=1.0467\times10^{-7}=1.05\times10^{-7}\text{s}^{-1}$

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 "Long Answer Type Questions [5M]" from Nuclei→Nuclei — all question types→Physics STD 12 Science question papers→Bihar Board STD 12 Science question papers→Bihar Board question paper generator→

Similar questions

A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror.
→
A cylindrical vessel of diameter 12cm contains $800\pi\text{cm}^3$ of water. A cylindrical glass piece of diameter 8.0 cm and height 8.0cm is placed in the vessel. If the bottom of the vessel under the glass piece is seen by the paraxial rays, locate its image. The index of refraction of glass is 1.50 and that of water is 1.33.

→
A smooth wedge A is fitted in a chamber hanging from a fixed ceiling near the earth's surface. A block B placed at the top of the wedge takes a time T to slide down the length of the wedge. If the block is placed at the top of the wedge and the cable supporting the chamber is broken at the same instant, the block will:
  1. Take a time longer than T to slide down the wedge.
  2. Take a time shorter than T to slide down the wedge.
  3. Remain at the top of the wedge.
  4. Jump off the wedge.
→
  1. Draw a ray diagram to show refraction of a ray of monochromatic light passing through a glass prism.

Deduce the expression for the refractive index of glass in terms of angle of prism and angle of minimum deviation.

  1. Explain briefly how the phenomenon of total internal reflection is used in fibre optics.
→
Two particles A and B having charges q and 2q respectively are placed on a smooth table with a separation d. A third particle C is to be clamped on the table in such a way that the particles A and B remain at rest on the table under electrical forces. What should be the charge on C and where should it be clamped?
→
A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12 cm from P. At what point does the beam converge if the lens is (a) a convex lens of focal length 20 cm, and (b) a concave lens of focal length 16 cm?
→
The two square faces of a rectangular dielectric slab (dielectric constant 4.0) of dimensions 20cm × 20cm × 1.0mm are metal-coated. Find the capacitance between the coated surfaces.
→
An electron makes 3 × 105 revolutions per second in a circle of radius 0.5 angstrom. Find the magnetic field B at the centre of the circle.
→
(a) Obtain an expression for current flowing through an ideal inductor joined with an ac source of voltage $v=v_0 \sin \omega t$ by using phasor diagram. Draw a graph between (i) voltage applied and (ii) current as a function of (wt.).
(b) Obtain an expression for average power dissipation in any series LCR circuit.
→
Two masses m1 and m2 are connected by a spring of spring constant k and are placed on a frictionless horizontal surface. Initially the spring is stretched through a distance x0 when the system is released from rest. Find the distance moved by the two masses before they again come to rest.
→