91影视

The mass of the sample, m = 1 kg

The energy, Q = 200 MeV

The lamp power, P = 100 W

The molar mass of uranium, M =235

The equation to calculate the number of the atoms in the sample is given as follows.

$\mathit{N}\mathbf{=}\frac{\mathbf{m}{\mathbf{N}}_{\mathbf{A}}}{\mathbf{M}}$ ...(i)

Here, is the Avogadro number $\left(6.02脳{10}^{23}{\mathrm{mol}}^{-1}\right)$ and M is the molar number.

The expression to calculate the released energy is given as follows.

E = NQ ...(ii)

The expression to calculate the how long energy can light a lamp is given as follows.

$\mathit{t}\mathbf{=}\frac{\mathbf{E}}{\mathbf{P}}$ ...(iii)

Calculate the number of the atoms.

Substitute 235 for M, 1 kg for m and $6.022脳{10}^{23}{\mathrm{mol}}^{-1}$for $N_A$into equation (i).

$$\begin{gathered} N=\frac{1000脳6.022脳{10}^{23}}{235} \\ N=\frac{6022脳{10}^{23}}{235} \\ N=25.62脳{10}^{23} \\ N=2.56脳{10}^{24} \end{gathered}$$

Hence the number of the atoms are $2.56脳{10}^{24}$.

Calculate the released energy.

Substitute$2.56脳{10}^{24}$ for N and 200 MeV for Q into equation (ii).

$$\begin{gathered} \mathrm{E}=2.56脳{10}^{24}脳100\mathrm{MeV} \\ \mathrm{E}=5.12脳{10}^{26}\mathrm{MeV} \\ \mathrm{E}=5.12脳{10}^{26}\mathrm{eV} \\ \mathrm{E}=8.2脳{10}^{13}\mathrm{J} \end{gathered}$$

Hence the released energy is $8.2脳{10}^{13}\mathrm{J}$.

Calculate the time.

Substitute$8.2脳{10}^{13}\mathrm{J}$ for E and 100 W for P into equation (iii)

$$\begin{gathered} \mathrm{t}=\frac{8.2脳{10}^{13}\mathrm{J}}{100\mathrm{W}} \\ \mathrm{t}=8.2脳{10}^{11}\sec \end{gathered}$$

Hence the 100 W lamp can light for$8.2脳{10}^{11}\sec$ .