Chapter 42: Q. 15 (page 1236)

Use the potential-energy diagram in Figure $42.8$ to estimate the ratio of the gravitational potential energy to the nuclear potential energy for two neutrons separated by $1.0$ $f m$ .

Short Answer

Expert verified

Ratio of gravitational potential energy to the nuclear potential energy is

$- 0.822 \times 10^{- 27} .$

Step by step solution

Given information.

We have been given that,

Two neutrons are separated by $1.0 f m$ ,

Mass of neutron= $1.67493 \times 10^{- 27} K g$ .

We need to find the ratio of gravitational potential energy to the nuclear potential energy for the two neutrons.

Simplify.

The gravitational potential energy is given by,

$U_{g}$ $=$ $- \frac{G M m}{r}$

Since,

$M = m = 1.67493 \times 10^{- 27} K g$ $=$ mass of neutrons

Therefore, $G = 6.67 \times 10^{- 11} N k g^{- 2} m^{2}$ , $r = 1.0 f m$

Putting the values in formula,

$U_{g} = - \frac{6.67 \times 10^{- 11} \times {(1.67493 \times 10^{- 27})}^{2}}{1.0 \times 10^{- 15}} J / k g = - \frac{18.711 \times 10^{- 65}}{10^{- 15}} J / k g = - 18.711 \times 10^{- 50} J / k g$

Now,

The nuclear potential energy is given by,

$U_{e} = \frac{Κ q^{2}}{r} J / k g$

$= \frac{8.89 \times {(1.6 \times 10^{- 19})}^{2}}{10^{- 15}} J / k g = 22.758 \times 10^{- 23} J / k g$

Now,

$\frac{U_{g}}{U e} = \frac{- 18.711 \times 10^{- 50}}{22.758 \times 10^{- 23}} = - 0.822 \times 10^{- 27}$

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Use the potential-energy diagram in Figure $42.8$ to estimate the ratio of the gravitational potential energy to the nuclear potential energy for two neutrons separated by $1.0$ $f m$ .

Short Answer

Step by step solution

Given information.

Simplify.

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Use the potential-energy diagram in Figure 42.8to estimate the ratio of the gravitational potential energy to the nuclear potential energy for two neutrons separated by 1.0fm.

Short Answer

Step by step solution

Given information.

Simplify.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electric Charge Field and Potential

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Study anywhere. Anytime. Across all devices.

Use the potential-energy diagram in Figure $42.8$ to estimate the ratio of the gravitational potential energy to the nuclear potential energy for two neutrons separated by $1.0$ $f m$ .