It takes 8.53 ✕ 10-19 j of energy to remove one electron from a certain metal surface. what is the maximum wavelength of light capable of causing this effect?

λ  = 233 nm

Explanation:

Step 1: Data given

8.53 * 10^-19 J of energy needed to remove 1 electron

Step 2: Calculate the wavelength

The energy of a photon is proportional to its frequency.

Mathematically, the relationship between the energy of a photon and its frequency is described by the Planck - Einstein equation:

E = h*f

⇒ E = the energy of the photon

⇒ h = Planck's constant, equal to  6.626  * 10 ^-34 J*s

⇒ f = the frequency

Frequency and wavelength have an Inverse relationship and can be described by the equation:

f*λ = c

⇒ λ = the wavelength of the photon

⇒ c = the speed of light in a vacuum, usually given as  3 *10 ^8  m/s

ν *λ  =  c  ⇒  ν =  c /λ

E  = h  *c /λ

λ  =( h ⋅*c )/E

λ  =  (6.626  * 10 ^-34 J*s * 3 *10 ^8  m/s) / 8.53 * 10^-19

λ  = 2.33 *10^-7 m

λ  = 233 nm

This wavelength places you in the ultraviolet - shortwave UV region of the EM spectrum.

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