Mock Test 1 — Atoms and Nuclei

The ratio of speeds of electron in 1st orbits of H and He$^+$:

The ratio of areas of 2nd and 3rd Bohr orbits:

The energy required to ionize He$^+$ from ground state:

A radioactive sample has half-life $5$ days. After $20$ days, $1/N$ remains. $N$ =:

The number of $\alpha$ and $\beta^-$ particles released in $^{238}$U to $^{206}$Pb:

The energy released in fusion of $4$ H to $^4$He is approximately:

The first line of Lyman series of hydrogen has wavelength:

The total spectral lines from $n = 6$ to ground in hydrogen:

The nuclear radius of $^{64}$Cu (in fm):

Binding energy per nucleon is maximum for:

Number of spectral lines from electron going from $n = 5$ to ground:

The ratio of radii of $^{27}$Al and $^{1}$H nuclei (use $27^{1/3} = 3$):

Activity reduces from $1000$ Bq to $125$ Bq in $9$ hours. Half life in hours:

Assertion (A): Energy is released in both fission of heavy nuclei and fusion of light nuclei. Reason (R): Binding energy per nucleon peaks at intermediate $A$, so reactions toward this peak release energy.

Assertion (A): Density of nuclear matter is the same for all nuclei. Reason (R): Nuclear radius $R \propto A^{1/3}$, so volume $\propto A$.