Advertisements
Advertisements
प्रश्न
Consider the decay of a free neutron at rest : n → p + e–
Show that the two-body decay of this type must necessarily give an electron of fixed energy and, therefore, cannot account for the observed continuous energy distribution in the β-decay of a neutron or a nucleus
उत्तर १
The decay process of free neutron at rest is given as:
n → p + e–
From Einstein’s mass-energy relation, we have the energy of electron as Δmc2
Where,
Δm = Mass defect = Mass of neutron – (Mass of proton + Mass of electron)
c = Speed of light
Δm and c are constants. Hence, the given two-body decay is unable to explain the continuous energy distribution in the β-decay of a neutron or a nucleus. The presence of neutrino νon the LHS of the decay correctly explains the continuous energy distribution.
उत्तर २
Let the masses of the electron and proton be m and M respectively. Let v and V be the velocities of electron and proton respectively. Using law of conservation of momentum. Momentum of electron + momentum of proton = momentum of neutron
`:. mv + MV = 0 => V = - m/M v`
Clearly the electron and the proton move in opposite directions. If mass `trianglem` has been conveted into energy in the reaction then
`1/2mv^2 + 1/2 MV^2 = trianglem xx c^2`
or `1/2mv^2 + 1/2M[-m/M]^2v^2 = trianglemc^2`
or `1/2mv^2[1+m/M] = trianglemc^2`
or `v^2 = (2Mtrianglemc^2)/(m(M+m))`
Thus, it is proved that the value of v2 is fixed since all the quantities in right hand side are constant. It establishes that the emitted electron must have a fixed energy and thus we cannot account for the continuous energy distribution in the β-decay of a neutron.
APPEARS IN
संबंधित प्रश्न
The bob A of a pendulum released from 30° to the vertical hits another bob B of the same mass at rest on a table, as shown in the figure. How high does the bob A rise after the collision? Neglect the size of the bobs and assume the collision to be elastic.
A bullet of mass 0.012 kg and horizontal speed 70 m s–1 strikes a block of wood of mass 0.4 kg and instantly comes to rest with respect to the block. The block is suspended from the ceiling by means of thin wires. Calculate the height to which the block rises. Also, estimate the amount of heat produced in the block.
Answer the following question.
Obtain its value for an elastic collision and a perfectly inelastic collision.
Answer the following question.
Discuss the following as special cases of elastic collisions and obtain their exact or approximate final velocities in terms of their initial velocities.
- Colliding bodies are identical.
- A very heavy object collides on a lighter object, initially at rest.
- A very light object collides on a comparatively much massive object, initially at rest.
A particle of mass 'm' collides with another stationary particle of mass 'M'. A particle of mass 'm' stops just after collision. The coefficient of restitution is ______.
A block of mass 'm' moving along a straight line with constant velocity `3vec"v"` collides with another block of same mass at rest. They stick together and move with common velocity. The common velocity is ______.
A smooth sphere of mass 'M' moving with velocity 'u' directly collides elastically with another sphere of mass 'm' at rest. After collision, their final velocities are V' and V respectively. The value of V is given by ______.
In an elastic collision of two billiard balls, which of the following quantities remain conserved during the short time of collision of the balls (i.e., when they are in contact).
- Kinetic energy.
- Total linear momentum?
Give reason for your answer in each case.
A ball is thrown upwards from the foot of a tower. The ball crosses the top of tower twice after an interval of 4 seconds and the ball reaches ground after 8 seconds, then the height of tower is ______ m. (g = 10 m/s2)
An insect moves with a constant velocity v from one corner of a room to other corner which is opposite of the first corner along the largest diagonal of room. If the insect can not fly and dimensions of room is a × a × a, then the minimum time in which the insect can move is `"a"/"v"`. times the square root of a number n, then n is equal to ______.
