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Chemistry: The Central Science | 13th Edition | ISBN: 9780321910417 | Authors: Theodore E. Brown; H. Eugene LeMay; Bruce E. Bursten; Catherine Murphy; Patrick Woodward; Matthew E. Stoltzfus
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Titanium metal requires a photon with a minimum energy of

Chapter , Problem 6.34

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QUESTION:

Titanium metal requires a photon with a minimum energy of 6.94 * 10 - 19 J to emit electrons. (a) What is the minimum frequency of light necessary to emit electrons from titanium via the photoelectric effect? (b) What is the wavelength of this light? (c) Is it possible to eject electrons from titanium metal using visible light? (d) If titanium is irradiated with light of wavelength 233 nm, what is the maximum possible kinetic energy of the emitted electrons? (d) What is the maximum number of electrons that can be freed by a burst of light whose total energy is 2.00 mJ?

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QUESTION:

Titanium metal requires a photon with a minimum energy of 6.94 * 10 - 19 J to emit electrons. (a) What is the minimum frequency of light necessary to emit electrons from titanium via the photoelectric effect? (b) What is the wavelength of this light? (c) Is it possible to eject electrons from titanium metal using visible light? (d) If titanium is irradiated with light of wavelength 233 nm, what is the maximum possible kinetic energy of the emitted electrons? (d) What is the maximum number of electrons that can be freed by a burst of light whose total energy is 2.00 mJ?

ANSWER:

Problem 6.34

Titanium metal requires a photon with a minimum energy of 6.94 \times 10^{-19} \text {J} to emit electrons.

(a) What is the minimum frequency of light necessary to emit electrons from titanium via the photoelectric effect? (b) What is the wavelength of this light? (c) Is it possible to eject electrons from titanium metal using visible light? (d) If titanium is irradiated with light of wavelength 233 nm, what is the maximum possible kinetic energy of the emitted electrons? (d) What is the maximum number of electrons that can be freed by a burst of light whose total energy is 2.00 mJ?

                                                              Step by Step Solution

Step 1 of 4

(a)

The mathematical relationship between energy and frequency is as follows.

                                                          $$ \mathrm {E= h \nu}........................................(1)

                                                           E = Energy

                                                           h  = Plank’s constant

                                                           v  = Frequency

Rearrange the equation (1) is as follows.

                                                            $$ \mathrm {\nu= \frac {E}{h} }...........................................(2)

From the given,

$$ \text{E} = 6.94 \times10^{-19}

$$ \text{h} = 6.626 \times 10^{-34} \text {J.s}

Substitute the values in equation (2)

                                                              $$ =\frac{6.94\times 10^{-19}\text{J}}{6.626 \times 10^{-34} \text {J.s}} = 1.05\times 10^{15} \text{Hz}

Therefore, the minimum frequency of light necessary to emit electrons from titanium via the photoelectric effect is 1.05\times 10^{15} \text{Hz}.

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