Energy of an atom in an excited state

[mstud]

Homework Statement

An atom which is in an excited state, can emit a photon with the wavelength of 330 nm at during the movement between two "energy niveaus". The last niveau has the energy $$-4.8 \cdot 10^{-19}J$$. What is the energy of the atom in the excited state?

Homework Equations

Not relevant for my conseptual question, but for solving the problem

the wave formula:$$c=f \lambda$$ and the formula for the energy of the photon$$E_{photon} =hf$$ where $$h=6.63 \cdot 10^{-34}$$

Also Bohrs formula: $$E_{state}=-\frac{B}{n^2}$$ where n is the number of the state

The Attempt at a Solution

I just wonder if I have understood the problem right...

I can use the wavelength to find the energy of the emitted photon . Then I combine the formula for the energy of the photon with Bohrs formula to find the energy of the atom in the excited state, right?

The energy in the excited state will be the energy in the last niveau plus the energy of the emitted photon, won't it?

These are my calculations:

The frequency for the emitted photon: $$c=f\lambda$$ gives $$f=\frac{c}{\lambda}=\frac{3.00 \cdot 10^8 m/sec}{330 \cdot 10^{-9} m}= 9.09 \cdot 10^{14} s^{-1}= 9.09 \cdot 10^{14} Hz$$

The energy of the photon: $$E_{photon} = 6.63 \cdot 10^{-34} Js \cdot 9.09 s^{-1} = 6.03 \cdot 10^{-19}$$

The energy of the atom in the excited state: $$E_{excited}=-4.8 \cdot 10^{-19} J + 6.03 \cdot 10^{-19}=1.23 \cdot 10^{-19}$$

However the answer shall be, according to my book: $$-0,17 \cdot 10^{-18} J$$ (I also know I shouldn't have got a positive answer)

Can anybody see what has gone wrong?

 

[mstud]

There was an error in my book.

The energy of the last niveau should be $-7.7 \cdot 10^{-19}$ in the problem text.

Thus my problem is now solved