Question

An electron is confined to a one dimensional infinite potential well 150 pm. How much energy must it absorb if it is to jump to the state n-3 from ground state?

Answer 1

\Delta E=1.22\times 10^{-22}J

Step-by-step explanation:

The energy of electron in any state is given by
`E=(n^2h^2)/(8mL^2)` here h is planck's constant n is state of electron L is the infinte potential well m is the mass of electron

We know that
`h=6.67* 10^(-34)`

Potential well dimension =
`150pm=150* 10^(-12)m`

Mass of electron
`=9.1* 10^(-31)kg`

So energy required to electron to jump from ground state to 3rd state

`\Delta E=(h^2)/(8mL^2)\left ( 3^2-1^2 \right )`

`\Delta E=(\left ( 6.67* 10^(-34) \right )^2)/(8* 9.1* 10^(-31)(150* 10^(-12))^2)\left ( 9-1 \right )`

`\Delta E=1.22* 10^(-22)J`