Scientists have recently discovered a strange new material called joelium, an electrical conductor whose mobile charges are joelons instead of electrons. The joelon has a charge of 3 times that of the electron and a mass of 7.88 times that of the electron. Assuming the other constants are the same:

What is the charge mobility of joelium relative to an ordinary conductor? 


What is the conductivity of joelium relative to an ordinary conductor? 

To address the questions, we will calculate the relative charge mobility and conductivity of joelium compared to an ordinary conductor. We'll base our calculations on the relationship between charge mobility, conductivity, and the properties of joelons versus electrons.

### 1. **Charge Mobility of Joelium Relative to an Ordinary Conductor**

Charge mobility (\( \mu \)) is defined as the drift velocity per unit electric field:

\[
\mu = \frac{v_d}{E}
\]

Mobility is inversely proportional to the mass of the charge carrier and directly proportional to the charge:

\[
\mu \propto \frac{q}{m}
\]

Where:
- \( q \) is the charge of the carrier,
- \( m \) is the mass of the carrier.

For joelons compared to electrons:
- The charge of a joelon is \( 3 \times \) the charge of an electron, i.e., \( q_j = 3q_e \),
- The mass of a joelon is \( 7.88 \times \) the mass of an electron, i.e., \( m_j = 7.88m_e \).

Thus, the relative mobility \( \mu_{\text{rel}} \) of joelons compared to electrons is:

\[
\mu_{\text{rel}} = \frac{q_j / m_j}{q_e / m_e} = \frac{3q_e / 7.88m_e}{q_e / m_e} = \frac{3}{7.88}
\]

\[
\mu_{\text{rel}} \approx 0.3807
\]

So, the mobility of joelons is approximately **38.1%** of the mobility of electrons.

### 2. **Conductivity of Joelium Relative to an Ordinary Conductor**

Conductivity (\( \sigma \)) is related to the number of charge carriers (\( n \)), the charge (\( q \)), and the mobility (\( \mu \)):

\[
\sigma = nq\mu
\]

Assuming the number density \( n \) of joelons and electrons is the same, the relative conductivity \( \sigma_{\text{rel}} \) will be proportional to the product of the charge and mobility:

\[
\sigma_{\text{rel}} = \frac{q_j \mu_j}{q_e \mu_e}
\]

We know that \( q_j = 3q_e \) and \( \mu_{\text{rel}} \approx 0.3807 \), so:

\[
\sigma_{\text{rel}} = \frac{3q_e \times 0.3807\mu_e}{q_e \times \mu_e} = 3 \times 0.3807 = 1.1421
\]

Thus, the conductivity of joelium is approximately **1.1421 times** that of an ordinary conductor.

### Summary of Results:
- **Charge mobility of joelium**: \( 0.3807 \) times that of an ordinary conductor.
- **Conductivity of joelium**: \( 1.1421 \) times that of an ordinary conductor.

Let me know if you'd like more details, or if you have any questions!

### Related Questions:
1. How does temperature affect the mobility of charge carriers like joelons?
2. What other factors might influence the conductivity of joelium aside from charge and mass?
3. How does the drift velocity of joelons compare to that of electrons in a conductor?
4. What implications could the higher conductivity of joelium have for practical applications?
5. Can the number density of joelons be altered to further improve conductivity?

### Tip:
Mobility is typically affected by factors like temperature and impurity scattering in the material, so improving these conditions can further enhance conductivity.

Scientists have recently discovered a strange new material called joelium, an electrical conductor whose mobile charges are joelons instead of electrons. The joelon has a charge of 3 times that of the electron and a mass of 7.88 times that of the electron. Assuming the other constants are the same: What is the charge mobility of joelium relative to an ordinary conductor? What is the conductivity of joelium relative to an ordinary conductor?

This problem involves calculating the charge mobility and conductivity of joelium, a newly discovered material with unique charge carriers called joelons. Learn how the charge mobility of joelons (approximately 38.1% of electrons) and their conductivity (1.1421 times that of ordinary conductors) compare, using key physics principles and formulas.

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