91影视

Power is, $I=5.0脳{10}^{-3}\text{W}$.

Diameter is, $d=1266脳{10}^{-9}\text{m}$.

Density is, $蚁=5000{\text{kg/m}}^{\text{3}}$.

Intensity is the power transferred per unit area, where the area is measured on the plane perpendicular to the direction of the propagation of the energy. The intensity or flux of radiant energy is the power transferred per unit area, where the area is measured on the plane perpendicular to the direction of propagation of the energy. In the SI system, it has a unit of watts per square meter or kg鈰卻鈦宦� in base units.

Intensity (I),

$I=\frac{\text{Power}}{\text{Area}}$

Radiation pressure (P_r),

$P_r=\frac{I}{c}$

Where, I is the intensity, P_r is the radiation pressure, and c is the speed of light.

Intensity (I)can be calculated as,

$I=\frac{P}{\frac{蟺d^2}{4}}$

Substitute the values in the above expression, and we get,

$$\begin{gathered} I=\frac{5.0脳{10}^{-3}}{\frac{蟺{\left(1266脳{10}^{-9}\right)}^2}{4}} \\ I=3.974脳{10}^9{\text{W/m}}^{\text{2}} \end{gathered}$$

Therefore, the beam intensity at the sphere鈥檚 location is $\text{3.974}脳{\text{10}}^{\text{9}}{\text{W/m}}^{\text{2}}$.

Radiation pressure(P_r)can be calculated as,

$P_r=\frac{I}{c}$

$\begin{array}{l}{P}_r=\frac{(3.974脳{10}^9)}{3脳{10}^8}\\ P_{\text{r}}=13.2\text{鈥塒补}\end{array}$

Therefore, the radiation pressure on the sphere is 13.25Pa.

The magnitude of the force (F_r) can be calculated as,

$F_r=P_r脳\frac{蟺d^2}{4}$

$$\begin{gathered} F_r=13.25脳蟺脳\frac{{\left(1266脳{10}^{-9}\right)}^2}{4} \\ {F}_r=1.667脳{10}^{-11}\text{N} \end{gathered}$$

Therefore, the magnitude of the corresponding force is$\text{1.667}脳{\text{10}}^{\text{-11}}\text{鈥塏}$

Mass can be calculated as,

$\left(m\right)=\frac{蚁脳蟺d^3}{6}$

Substitute the values in the above expression, and we get,

$$\begin{gathered} m=\frac{5000脳蟺脳{\left(1266脳{10}^{-9}\right)}^2}{6} \\ m=5.31脳{10}^{-15}\text{kg} \end{gathered}$$

To find the acceleration of the sphere (a), we can use the equation as,

$a=\frac{F_r}{m}$

Substitute the values in the above expression, and we get,

$$\begin{gathered} a=\frac{1.667脳{10}^{-11}}{5.31脳{10}^{-15}} \\ a=3.14脳{10}^3{\text{m/s}}^{\text{2}} \end{gathered}$$

Therefore, the magnitude of the acceleration that force would give the sphere is $\text{3.14}脳{\text{10}}^{\text{3}}{\text{m/s}}^{\text{2}}$.