- #1
Lancelot59
- 646
- 1
I'm given a form of Heisenberg's uncertainty principle in the form of:
[tex]\Delta E\Delta t\geq h[/tex]
I need to determine a time interval which would allow a laser to cover the whole visible spectrum, from 400 to 700nm.
Now given the relationship is on on a relative scale I used the approximation:
[tex]\Delta E\Delta t\approx h[/tex]
I then used the following formula:
[tex]E=\frac{hc}{\lambda}[/tex]
and differentiated like so:
[tex]\Delta E = -\frac{hc}{\lambda ^{2}}\Delta \lambda[/tex]
Which I then substituted back in:
[tex](-\frac{hc}{\lambda ^{2}}\Delta \lambda)\Delta t \approx h[/tex]
Is this correct so far?
[tex]\Delta E\Delta t\geq h[/tex]
I need to determine a time interval which would allow a laser to cover the whole visible spectrum, from 400 to 700nm.
Now given the relationship is on on a relative scale I used the approximation:
[tex]\Delta E\Delta t\approx h[/tex]
I then used the following formula:
[tex]E=\frac{hc}{\lambda}[/tex]
and differentiated like so:
[tex]\Delta E = -\frac{hc}{\lambda ^{2}}\Delta \lambda[/tex]
Which I then substituted back in:
[tex](-\frac{hc}{\lambda ^{2}}\Delta \lambda)\Delta t \approx h[/tex]
Is this correct so far?