To identify the emitted particles, let us verify the conservation of atomic number (\(Z\)) and mass number (\(A\)).
- Atomic number (\(Z\)):
\[ Z_{\text{LHS}} = 92, \quad Z_{\text{RHS}} = 56 + 36 = 92 \]
\(Z\) is conserved.
- Mass number (\(A\)):
\[ A_{\text{LHS}} = 236, \quad A_{\text{RHS}} = 141 + 92 = 233 \]
The mass number is not conserved. The difference is:
\[ A_{\text{LHS}} - A_{\text{RHS}} = 236 - 233 = 3 \]
The missing mass corresponds to three neutrons (\(R = \text{neutrons}\)).
Match the LIST-I with LIST-II
LIST-I (Type of decay in Radioactivity) | LIST-II (Reason for stability) | ||
---|---|---|---|
A. | Alpha decay | III. | Nucleus is mostly heavier than Pb (Z=82) |
B. | Beta negative decay | IV. | Nucleus has too many neutrons relative to the number of protons |
C. | Gamma decay | I. | Nucleus has excess energy in an excited state |
D. | Positron Emission | II. | Nucleus has too many protons relative to the number of neutrons |
Choose the correct answer from the options given below:
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The density of the copper ($^{64}Cu$) nucleus is greater than that of the carbon ($^{12}C$) nucleus.
Reason (R): The nucleus of mass number A has a radius proportional to $A^{1/3}$.
In the light of the above statements, choose the most appropriate answer from the options given below:
Choose the correct set of reagents for the following conversion:
A bead of mass \( m \) slides without friction on the wall of a vertical circular hoop of radius \( R \) as shown in figure. The bead moves under the combined action of gravity and a massless spring \( k \) attached to the bottom of the hoop. The equilibrium length of the spring is \( R \). If the bead is released from the top of the hoop with (negligible) zero initial speed, the velocity of the bead, when the length of spring becomes \( R \), would be (spring constant is \( k \), \( g \) is acceleration due to gravity):