• xregina12
In summary, the uncertainty relation for time and energy, ΔEΔt > h/4π, can be applied to calculate the uncertainty in frequency associated with an emitted photon. In this case, the average lifetime of an excited state of an atom responsible for photon emission is 10^-10 s. By setting ΔE=hΔv, the calculated value for Δv may seem large compared to the frequency of visible light (1014-1015 Hz). This suggests that further guidance may be needed to accurately calculate the uncertainty in frequency.

#### xregina12

Analogous to the uncertainty relation ΔpΔx > h/4π, there is an uncertainty relation for the time and energy, ΔEΔt > h/4π that stems from the methods
usually used to measure the energy. The uncertainty in the time, Δt, can be interpreted as a lifetime. The excited state of an atom responsible for the emission of a photon has an average lifetime of 10^-10 s. What is the corresponding uncertainty in the frequency associated with the emitted photon?

What I understood based on the uncertainty principle:
ΔEΔt > h/4π and that Δt=10^-10 s here in this problem.
I can use this to calculate ΔE.
However, my next step is something I am not sure about. I set ΔE=hΔv and solved for v but then got 7.96x10^8 ms-1 which is so big and doesn't make sense to me.

Can anyone explain what I did wrong, why, and give me some guidance on what I should do to get the uncertainty in frequency?

xregina12 said:
What I understood based on the uncertainty principle:
ΔEΔt > h/4π and that Δt=10^-10 s here in this problem.
I can use this to calculate ΔE.
However, my next step is something I am not sure about. I set ΔE=hΔv and solved for v but then got 7.96x10^8 ms-1 which is so big and doesn't make sense to me.

Can anyone explain what I did wrong, why, and give me some guidance on what I should do to get the uncertainty in frequency?
Do you mean for the units to be s-1 or ms-1?

Either way, consider that visible light has a frequency in the range of 1014-1015 Hz (or s-1). Compared to that, does your Δv value appear to be large or small?

## 1. What is the uncertainty principle?

The uncertainty principle, also known as Heisenberg's uncertainty principle, states that it is impossible to know the exact position and momentum of a subatomic particle at the same time. This is due to the inherent uncertainty and unpredictability of quantum mechanics.

## 2. Who discovered the uncertainty principle?

The uncertainty principle was first proposed by German physicist Werner Heisenberg in 1927.

## 3. How does the uncertainty principle affect our understanding of the universe?

The uncertainty principle has significant implications for our understanding of the universe, as it challenges the classical laws of physics and introduces a level of uncertainty and randomness at the subatomic level. It also plays a crucial role in quantum mechanics and our understanding of the behavior of particles.

## 4. Can the uncertainty principle be observed in everyday life?

While the uncertainty principle is typically only observed at the subatomic level, it can also be observed in larger systems. For example, the movement of large molecules in a gas can exhibit uncertainty due to their small size and rapid movement.

## 5. How does the uncertainty principle relate to other principles in physics?

The uncertainty principle is closely related to other principles in physics, such as the principle of complementarity and the wave-particle duality. These principles all contribute to our understanding of the behavior of particles and the nature of the universe at a fundamental level.