Question

Hi
Theres a few questions i need to checkmy work on. the questions are
1.What is the frequency of a photon with a wavelength of 1040 nm. Report your answers to three significant digits.
The frequency is = _________ s-1

2.What is the energy of a photon with a wavelength of 260 nm. Report your answers to three significant digits.

3.In the Bohr model of the hydrogen atom, the n=1 to n=4 electronic transition corresponds with an ______ of energy; the change in the energy of the atom in this process is a _______ value.

Answer 1

Answer on Question #48374-Physics-Atomic Physics

1. What is the frequency of a photon with a wavelength of $\lambda = 1040\ nm$. Report your answers to three significant digits.

The frequency is = ________ s-1

2. What is the energy of a photon with a wavelength of $260\ \mathrm{nm}$. Report your answers to three significant digits.

3. In the Bohr model of the hydrogen atom, the $n=1$ to $n=4$ electronic transition corresponds with an ______ of energy; the change in the energy of the atom in this process is a ______ value.

Solution

1. The frequency of a photon is

$$f = \frac{c}{\lambda} = \frac{3 \cdot 10^{8} \frac{m}{s}}{1040 \cdot 10^{-9} m} = 2.88 \cdot 10^{14} \ \mathrm{Hz}.$$

2. The energy of a photon is

$$E = hf = h \frac{c}{\lambda} = 6.63 \cdot 10^{-34} J \cdot s \cdot \frac{3 \cdot 10^{8} \frac{m}{s}}{260 \cdot 10^{-9} m} = 7.65 \cdot 10^{-19} J.$$

3. According to Bohr's equation, the energy change for the atom is

$$\Delta E = R \left(\frac{1}{1^{2}} - \frac{1}{4^{2}}\right) = 2.179 \cdot 10^{-18} \left(\frac{15}{16}\right) J = 2.04 \cdot 10^{-18} J.$$

In the Bohr model of the hydrogen atom, the $n=1$ to $n=4$ electronic transition corresponds with an increasing of energy; the change in the energy of the atom in this process is a $2.04 \cdot 10^{-18} J$ value.

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