For a hydrogen atom, calculate the energy of the photon that would be emitted for the orbital transition of n(initial) = 5 to n(final) = 2. The Rydberg constant is 1.09678 x 10² m-¹.
Atomic Structure
The basic structure of an atom is defined as the component-level of atomic structure of an atom. Precisely speaking an atom consists of three major subatomic particles which are protons, neutrons, and electrons. Many theories have been stated for explaining the structure of an atom.
Shape of the D Orbital
Shapes of orbitals are an approximate representation of boundaries in space for finding electrons occupied in that respective orbital. D orbitals are known to have a clover leaf shape or dumbbell inside where electrons can be found.
![**Question 1 of 21**
For a hydrogen atom, calculate the energy of the photon that would be emitted for the orbital transition of n(initial) = 5 to n(final) = 2. The Rydberg constant is \(1.09678 \times 10^7 \, \text{m}^{-1}\).
**Explanation:**
This question involves calculating the energy of a photon emitted when an electron transitions between energy levels in a hydrogen atom. Specifically, it asks for the energy when an electron drops from the 5th energy level (n=5) to the 2nd energy level (n=2). The Rydberg constant provided is crucial for this calculation.
**Calculation:**
To find the energy (E) of the emitted photon, we use the Rydberg formula for hydrogen:
\[
E = h \cdot c \cdot \left( \frac{1}{n_{\text{final}}^2} - \frac{1}{n_{\text{initial}}^2} \right) \cdot R
\]
Where:
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\))
- \(c\) is the speed of light (\(3.00 \times 10^8 \, \text{m/s}\))
- \(R\) is the Rydberg constant (\(1.09678 \times 10^7 \, \text{m}^{-1}\))
- \(n_{\text{final}}\) and \(n_{\text{initial}}\) are the final and initial energy levels, respectively.
The keypad shown illustrates where the answer is to be entered, with a field labeled "J" indicating the unit for energy (Joules).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38543b38-0ca2-4898-a226-639f5edfcbc9%2Fd180f573-1701-403d-b182-44e3e6df3dc4%2Fj7byo6_processed.jpeg&w=3840&q=75)
The electronic energy levels in an atom are quantized and when an electron undergoes a transition from a higher energy level to a lower energy level a photon of electromagnetic radiation is emitted. The series of the radiation in the emission spectrum is known as the hydrogen emission spectrum.
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