Which of the following is true for the transition of electrons from a higher energy to a lower energy state?
Choose one answer.
a. The greater the energy difference between the levels, the more is the wavelength of the photons emitted.
b. The greater the energy difference between the levels, the less is the wavelength of the photons emitted.
c. The greater the energy difference between the levels, the less is the frequency of the photons emitted.
d. The energy difference is not related to frequency or wavelength of the photons emitted.
change in energy = h f
where f is the frequency of the photon emitted and h is Planck constant.
T c = (1/f)c = wavelength
so f = c/wavelength
so
change in energy = hc/wavelength
so
big change in energy goes with small wavelength
That is all I will do without seeing your analysis and what your answers would be.
To determine which answer is true for the transition of electrons from a higher energy to a lower energy state, we need to understand the relationships between energy levels, wavelength, and frequency.
When an electron transitions from a higher energy state to a lower energy state, it emits a photon of light. The energy of this photon is directly related to the energy difference between the two states.
According to the equation E = hf, where E is the energy of a photon, h is Planck's constant (a fundamental constant in physics), and f is the frequency of the photon. Since we're dealing with photons of light, we can also use the equation c = λf, where c is the speed of light, λ is the wavelength, and f is the frequency again.
From these equations, we can infer the following:
a. The greater the energy difference between the levels, the more energy the emitted photon will have. The energy of a photon is inversely proportional to its wavelength (according to E = hf and c = λf). Therefore, the greater the energy difference, the shorter the wavelength of the photons emitted. Therefore, option a is incorrect.
b. The greater the energy difference between the levels, the less wavelength of the photons emitted. This statement matches our inference from the equation E = hf and c = λf. A greater energy difference means a higher energy photon, which corresponds to a shorter wavelength. Therefore, option b is correct.
c. The greater the energy difference between the levels, the less frequency of the photons emitted. This statement is not supported by our reasoning using the equations E= hf and c = λf. Frequency is a property of the emitted photon, which is determined by the energy difference between the levels. Therefore, option c is incorrect.
d. The energy difference is not related to the frequency or wavelength of the photons emitted. This statement is incorrect. As discussed earlier, the energy difference directly affects the energy, frequency, and wavelength of the emitted photons. Therefore, option d is incorrect.
In conclusion, the correct answer is b. The greater the energy difference between the levels, the less is the wavelength of the photons emitted.