Question

In: Chemistry

Be sure to answer all parts. Consider the following energy levels of a hypothetical atom: E4...

Be sure to answer all parts. Consider the following energy levels of a hypothetical atom: E4 −2.11 × 10−19 J E3 −8.11 × 10−19 J E2 −1.25 × 10−18 J E1 −1.55 × 10−18 J (a) What is the wavelength of the photon needed to excite an electron from E1 to E4? (b) What is the energy (in joules) a photon must have in order to excite an electron from E2 to E3? (c) When an electron drops from the E3 level to the E1 level, the atom is said to undergo emission. Calculate the wavelength of the photon emitted in this process.

Expert Solution

Given

E1 = - 1.55 * 10^-18 J

E2 = -1.25 * 10^-18 J

E3 = -8.11 * 10^-19 J = - 0;811 * 10^-18 J

E4 = - 2.55 * 10^-19J = - 0.255 * 10^-18 J

(a)

to get wavelength of photon needed to excite from E1 to E4 we need energy difference between E1 to E4

E1 - E4 = - 1.55 * 10^-18 J - (- 0.255 * 10^-18 J) = - 1.295 * 10^-18 J

Converting this to wavelength

E = hc /

where h = 6.626 * 10^-34 J.s planck's constant

c = 3 * 10^8 m/s velocity of light (photon)

E = 1.295 * 10^-18 J = hc /

6.626 * 10^-34 J.s * 3 * 10^8 m/s / = 1.295 * 10^-18 J

= 1.534 * 10^-7 m = 153.4 nm Wavelenght of photon needed to excite electron Answer (a)

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(b)

Energy for E2 to E3 = -1.25 * 10^-18 J - (-0.811 * 10^-18 J) = - 0.439 * 10^-18 J Answer (b)

the photon must have 0.439 * 10^-18 J to excite electron fromm E2 to E3

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(c)

E3 to E1 = -0.811 * 10^-18 J - (-1.55 * 10^-18 J) = 0.739 * 10^-18 J

E = 0.739 * 10^-18 J = hc /

6.626 * 10^-34 J.s * 3 * 10^8 m/s / = 0.739 * 10^-18 J

= 2.6898 * 10^-7 m = 268.98 nm

photon of wavelength 269 nm will be emitted when electron drops from E3 to E1 Answer

queen_honey_blossom answered 2 years ago

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