Chapter 25: Q. 14 (page 709)

What potential difference is needed to accelerate a $He +$ ion (charge $+ e, mass 4 u$ ) from rest to a speed of $2.0 \times 10^{6} m / s$ ?

Short Answer

Expert verified

$∆ V = 8.35 \times 10^{4} V$

Step by step solution

Given information and theory used

Given :

Element : $He +$ ion (charge $+ e, mass 4 u$ )

To accelerate to a speed of : $2.0 \times 10^{6} m / s$

Theory used :

From the equation of conservation of energy, we have :

$q ∆ V = \frac{m}{2} ({v_{f}}^{2} - {v_{i}}^{2})$

Calculating potential difference needed

Because all of the energy from the electric field is changed to kinetic energy, we get :

$q ∆ V = \frac{m {v_{f}}^{2}}{2}$

Taking into account the fact that there is no beginning velocity, we will have that. We may now write the solution as

$∆ V = \frac{m {v_{f}}^{2}}{2 q}$ .

The potential difference can be calculated as $∆ V = \frac{m {v_{2}}^{2}}{2 q}$ because the initial velocity is zero.

We get $∆ V$ by substituting the supplied numerical values :

$∆ V = \frac{4 \times 1.67 \times 10^{- 27} {(2 \times 10^{6})}^{2}}{2 \times 1.6 \times 10^{- 19}} ∆ V = 8.35 \times 10^{4} V$

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What potential difference is needed to accelerate a $He +$ ion (charge $+ e, mass 4 u$ ) from rest to a speed of $2.0 \times 10^{6} m / s$ ?

Short Answer

Step by step solution

Given information and theory used

Calculating potential difference needed

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What potential difference is needed to accelerate a He+ion (charge +e,mass4u) from rest to a speed of2.0×106m/s?

Short Answer

Step by step solution

Given information and theory used

Calculating potential difference needed

One App. One Place for Learning.

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What potential difference is needed to accelerate a $He +$ ion (charge $+ e, mass 4 u$ ) from rest to a speed of $2.0 \times 10^{6} m / s$ ?