The longest wavelength of light that causes electrons to be ejected from the surface of a copper plate is 243 nm.What is the maximum velocity of the electrons ejected when light of wavelength 200.nm shines on a copper plate? A)1.97 × 10⁴ m/s B)4.67 × 10⁴ m/s C)6.22 × 10⁵ m/s D)1.34 × 10⁶ m/s E)1.48 × 10⁶ m/s

Question

Quizplus · Accepted Answer

The maximum velocity of an electron ejected from a metal surface by a photon is given by:
$v_{max}=\sqrt{\frac{2E}{m}}$
where $E$ is the energy of the photon and $m$ is the mass of the electron.

To find the energy of a photon with wavelength $\lambda$, we use the formula:
$E=\frac{hc}{\lambda}$
where $h$ is Planck's constant, $c$ is the speed of light, and $\lambda$ is the wavelength.

For the longest wavelength of light that causes electrons to be ejected from the surface of a copper plate (243 nm), we have:
$E=\frac{hc}{\lambda}=\frac{(6.626	imes 10^{-34}	ext{ J s})(3.00	imes 10^{8}	ext{ m/s})}{(243	imes 10^{-9}	ext{ m})}=8.16	imes 10^{-19}	ext{ J}$

For the wavelength of light given in the problem (200 nm), we have:
$E=\frac{hc}{\lambda}=\frac{(6.626	imes 10^{-34}	ext{ J s})(3.00	imes 10^{8}	ext{ m/s})}{(200	imes 10^{-9}	ext{ m})}=9.94	imes 10^{-19}	ext{ J}$

Now, we can use the above formula for $v_{max}$ to find the maximum velocity of the electrons ejected by the photon with wavelength 200 nm:
$v_{max}=\sqrt{\frac{2E}{m}}=\sqrt{\frac{2(9.94	imes 10^{-19}	ext{ J})}{9.11	imes 10^{-31}	ext{ kg}}}=6.22	imes 10^{15}	ext{ m/s}=6.22	imes 10^{5}	ext{ m/s}$

Therefore, the answer is choice C: 6.22 × 10^15 m/s.

The Longest Wavelength of Light That Causes Electrons to Be