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The question asks for the energy and the radius of an electron in the fourth orbit of a hydrogen atom. These can be calculated using well-known formulas from the Bohr model of the hydrogen atom.

1. **Energy of the electron (in joules) in the nth orbit** is given by:
   \[
   E_n = \dfrac{-13.6 \, \text{eV}}{n^2}
   \]
   Where:
   - \( E_n \) is the energy in electron volts (eV).
   - \( n \) is the principal quantum number (in this case, \( n = 4 \)).
   - 1 eV = \( 1.602 \times 10^{-19} \) Joules.

2. **Radius of the orbit (in meters)** is given by:
   \[
   r_n = n^2 \cdot a_0
   \]
   Where:
   - \( r_n \) is the radius of the orbit.
   - \( a_0 = 0.529 \, \text{Å} \) (Bohr radius), which equals \( 0.529 \times 10^{-10} \, \text{m} \).
   - \( n \) is the principal quantum number.

I'll now calculate both the energy and the radius for the fourth orbit (n = 4).For the electron in the fourth orbit of a hydrogen atom:

1. The energy of the electron is approximately \(-1.36 \times 10^{-19} \, \text{J}\).
2. The radius of the orbit is approximately \(0.846 \, \text{nm}\).

Would you like further details or clarification on these calculations?

Here are five related questions:
1. How does the energy of the electron change with increasing orbit number?
2. What is the energy of the electron in the second orbit of the hydrogen atom?
3. How is the Bohr model limited when applied to multi-electron atoms?
4. What would the radius be for the electron in the third orbit of the hydrogen atom?
5. How does the radius of an orbit change with increasing principal quantum number?

**Tip:** The energy of an electron in a hydrogen atom becomes less negative (i.e., closer to zero) as the orbit number increases, meaning it takes less energy to remove the electron from the atom.

¿Cuál es la energía (en J) del electrón en la cuarta órbita del átomo de hidrógeno? ¿Cuál es el radio (en nm) de esta órbita?

Explore the calculations for the energy and radius of an electron in the fourth orbit of the hydrogen atom using the Bohr model. This problem covers quantum mechanics concepts and involves formulas for energy and radius.

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