Chapter 37: Q. 14 (page 1082)

Determine:
a. The speed of a $7.0 M e V$ neutron.
b. The speed of a $15 M e V$ helium atom.
c. The specific type of particle that has $1.14 k e V$ of kinetic energy when moving with a speed of localid="1648723450518" role="math" $2.0 \times 10^{7} m / s$ .

Short Answer

Expert verified

a. The speed of a $7.0 M e V$ is $3.7 \times 10^{7} m / s$ .

b. The speed of a $15 M e V$ is $2.67 \times 10^{7} m / s$ .

c. The specific type of particle is electron.

Step by step solution

Part (a) step 1: Given information

We need to determine the speed of a $7.0 M e V$ neutron.

Part (a) step 2: Simplify

Energy of motion is

$7.0 M e V = 7.0 \times 10^{6} \times 1.6 \times 10^{- 19} J m a s s m = 1.6 \times 10^{- 27} k g v = \sqrt{\frac{2 E_{k}}{m}} = \sqrt{\frac{2 \times 7.0 \times 10^{6} \times 1.6 \times 10^{- 19}}{1.6 \times 10^{- 27}}} = 3.7 \times 10^{7} m / s$

Part (b) step 1: Given information

We need to determine the speed of a $15 M e V$ helium atom.

Part (b) step 2: Simplify

Energy= $15.0 M e V = 15.0 \times 10^{6} \times 1.6 \times 10^{- 19} J$ ,

Mass= $6.64 \times 10^{- 27} k g$

Velocity $v$ is

$v = \sqrt{\frac{2 E_{k}}{m}} = \sqrt{\frac{2 \times 15.0 \times 10^{6} \times 1.6 \times 10^{- 19}}{6.64 \times 10^{- 27}}} = 2.67 \times 10^{7} m / s$

part (c) Given information

We need to determine the specific type of particle that has $1.14 M e V$ of kinetic energy when moving with a speed of localid="1648723371129" $2.0 \times 10^{7} m / s$ .

Part (c) step 2: Simplify

Energy= $1.14 K e V = 1.14 \times 10^{3} \times 1.6 \times 10^{- 19} J$

Velocity = $2.0 \times 10^{7} m / s$

$m = \frac{2 E_{k}}{v^{2}} = \frac{2 \times 1.14 \times 10^{3} \times 1.6 \times 10^{- 19}}{{(2.0 \times 10^{7})}^{2}} = 9.1 \times 10^{- 31}$

Since the mass of the particle is equal to electron, hence the unknown particle is electron.

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Determine:
a. The speed of a $7.0 M e V$ neutron.
b. The speed of a $15 M e V$ helium atom.
c. The specific type of particle that has $1.14 k e V$ of kinetic energy when moving with a speed of localid="1648723450518" role="math" $2.0 \times 10^{7} m / s$ .

Short Answer

Step by step solution

Part (a) step 1: Given information

Part (a) step 2: Simplify

Part (b) step 1: Given information

Part (b) step 2: Simplify

part (c) Given information

Part (c) step 2: Simplify

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Determine:a. The speed of a 7.0MeVneutron.b. The speed of a 15MeVhelium atom.c. The specific type of particle that has 1.14keVof kinetic energy when moving with a speed of localid="1648723450518" role="math" 2.0×107m/s.

Short Answer

Step by step solution

Part (a) step 1: Given information

Part (a) step 2: Simplify

Part (b) step 1: Given information

Part (b) step 2: Simplify

part (c) Given information

Part (c) step 2: Simplify

One App. One Place for Learning.

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Physical Quantities And Units

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Study anywhere. Anytime. Across all devices.

Determine:
a. The speed of a $7.0 M e V$ neutron.
b. The speed of a $15 M e V$ helium atom.
c. The specific type of particle that has $1.14 k e V$ of kinetic energy when moving with a speed of localid="1648723450518" role="math" $2.0 \times 10^{7} m / s$ .