In another universe the value of Plancks constant is 663 tim

In another universe the value of Planck\'s constant is 6.63 times 10^-22 Js. Assume that the physical laws and all other physical constants are the same as in our universe. In the other universe, an atom is in an excited state 4.50 eV above the ground state. The lifetime of this excited state (the average time the electron stays in this state) is 2.24 times 10^-3 s. What is the minimum uncertainty (in eV) in the energy of the photon emitted when the atom makes the transition from this excited state to the ground state?

Solution

Applying the time -Energy Uncentainty Relation:

(deltaT) (deltaE) >= h / (4 pi )

for minimum deltaE will be when deltaT is maximum.

maximum deltaT = 2.24 x 10^-3 s

(2.24 x 10^-3) (deltaEmin) = (6.63 x 10^-22 ) / (4 pi )

deltaE_min = 2.355 x 10^-20 J

in eV = (2.355 x 10^-20 ) / (1.6 x 10^-19) = 0.15 eV