 Find the electric potential difference ΔVe required to stop an electron (called a "stopping potential") moving with an initial speed of 2.10  107 m/s. in kV

The electric potential difference (\(\Delta V_e\)) required to stop an electron moving with an initial speed \(v_0 = 2.10 \times 10^7 \, \text{m/s}\) can be calculated using the principle of conservation of energy. Specifically, the kinetic energy of the electron is converted into electrical potential energy.

The kinetic energy (\(K.E.\)) of the electron is given by:

\[
K.E. = \frac{1}{2} m_e v_0^2
\]

where:
- \(m_e = 9.109 \times 10^{-31} \, \text{kg}\) is the mass of the electron,
- \(v_0 = 2.10 \times 10^7 \, \text{m/s}\) is the initial speed of the electron.

The electrical potential energy change is:

\[
\Delta U = e \Delta V_e
\]

where:
- \(e = 1.602 \times 10^{-19} \, \text{C}\) is the elementary charge (the charge of the electron),
- \(\Delta V_e\) is the potential difference.

Setting the kinetic energy equal to the change in electrical potential energy:

\[
\frac{1}{2} m_e v_0^2 = e \Delta V_e
\]

Solving for \(\Delta V_e\):

\[
\Delta V_e = \frac{\frac{1}{2} m_e v_0^2}{e}
\]

Now let's calculate \(\Delta V_e\).The electric potential difference (\(\Delta V_e\)) required to stop the electron is approximately \(1.25 \, \text{kV}\).

Would you like more details or have any questions? 

Here are 5 related questions you might explore:
1. How does the stopping potential vary with the speed of the electron?
2. What is the relationship between electric potential and kinetic energy?
3. How does the mass of a particle affect the stopping potential?
4. What happens if a proton is used instead of an electron in this scenario?
5. How do we measure stopping potential experimentally?

**Tip:** The stopping potential depends only on the speed of the particle, not its charge, as long as it's uniformly charged.

Find the electric potential difference ΔVe required to stop an electron (called a 'stopping potential') moving with an initial speed of 2.10 × 10^7 m/s. in kV

Discover how to calculate the electric potential difference (ΔVe) required to stop an electron moving at 2.10 × 10^7 m/s. This problem explores key physics concepts, including kinetic energy, electric potential energy, and the conservation of energy. Suitable for college-level physics students.

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