Alpha Decay

Q. 176 A bomb of mass 30 kg at rest explodes into two pieces of masses 18kg and 12kg. the velocity of18 kg mass is 6m/s. the kinetic energy of the other mass is

Q.

A bomb at rest on a horizontal frictionless surface explodes and breaks into three pieces that fly apart horizontally as shown below. Select all of the following statements that must be true after the bomb has exploded.

1. The total kinetic energy of the bomb fragments is the same as that of the bomb before explosion.
2. The total momentum of the bomb fragments is the same as that of the bomb before explosion.
3. The total momentum of all the bomb fragments together is zero.

1. 1 only

2. 3 only

3. 2 only

4. 1, 2, and 3

Q. In the beta decay of Na${}^{24}$, the combined electron neutrino momentum has a magnitude equal to 4 $\frac{Mev}{c}$. What is the recoil energy of the daughter nucleus, given that its mass is $23.99u?$
Take $[c=3\times {10}^8\text{m/s},1u=1.66\times {10}^{-27}\text{kg}]$

1. $2.78\times {10}^{-4}$ MeV
2. $3.56\times {10}^{-4}$ MeV
3. $0.72\times {10}^{-4}$ MeV
4. $1.25\times {10}^{-4}$ MeV

Q. A shell of mass 20kg at rest explodes into two fragments whose masses are in the ratio 2:3 . The smaller fragment moves with a velocity of 6m/s . The kinetic energy of large fragment is

Q. In a gamma decay process, the internal energy of a nucleus of mass M decreases, a gamma photon of energy E and linear momentum E/c is emitted and the nucleus recoils. Find the decrease in internal energy.

Q. ${}_{92}^{238}U\stackrel{\alpha }{\to }Y\stackrel{{}_{+}{\beta }^0}{\to }{}_Z^{A}X$, find A & Z.

1. Z = 87; A = 234
2. Z = 89; A = 234
3. Z = 89; A = 236
4. Z = 87; A = 232

Q. If 1/3 rd length of a chain of length l and mass m overhangs a smooth table with the other 2/rd resting on the table then what will be the kinetic energy of the chain as it completely slips of thre smooth table?

Q. The element Lawrencium ${(}_{103}^{256}Lr)$ is named after Ernest Lawrence, whose invention - the cyclotron - helped discover many radioactive nuclei. Consider now, the alpha decay of ${}_{103}^{256}Lr$:
${}_{103}^{256}Lr{\to }_b^{a}Md+\alpha ,$
Where $\alpha$ represents the alpha particle given out. What are the values of a and b?

1. a=252; b=105
2. a=252; b=101
3. a=260; b=101
4. a=260; b=105

Q. A uranium-238 nucleus, initially at rest, emits an alpha particle with a speed of 1.4 × 10⁷ m/s. Calculate the recoil speed of the residual nucleus thorium-234. Assume that the mass of a nucleus is proportional to the mass number.

Q. A nucleus with mass number 220 initially at rest emits an $\alpha$ -particle. If the Q value of the reaction is 5.5 MeV. Calculate the kinetic energy of the $\alpha$ -particle

1. 4.4 MeV
2. 5.4 MeV
3. 5.6 MeV
4. 6.5 MeV

Q. An isolated particle of mass m is moving in a horizontal x-y plane?along the x-axis at a certain height above the ground. It explodes suddenly into two fragments of masses m/4 and 3 m/4. An instant later, the smaller fragment is at y = + 15 cm. What is the position of larger fragment at this instant?

Q. give example of the body which possess momentum even when the total energy is negative

Q. A shell of mass 20kg at rest explodes into two fragments whose masses are in the ratio 2:3 . The smaller fragment moves with a velocity of 6m/s . The kinetic energy of large fragment is

Q. In a radioactive decay chain, ​${}_{90}^{232}Th$ nucleus decays to ${}_{82}^{212}Pb$ nucleus. Let $N_{\alpha }$ ​ and $N_{\beta }$ ​ be the number of α and ${\beta }^{-}$ particles respectively, emitted in this decay process. Which of the following statements is (are) true?

1. $N_{\alpha }=5$
2. $N_{\alpha }=6$
3. $N_{\beta }=2$
4. $N_{\beta }=4$