I need some help with this. The surface of a particular metal is initially exposed to light with a wavelength of X₁ = 350 nm and subsequently tolight with a wavelength of X₂ = 540 nm. It has been observed that the maximum speed of the emitted photoelectronsdiffers by a factor of 2 between the two cases. The work function of the metal (in eV) can be approximated usingthe formula:1240XWhich of the following values is closest to the work function of this metal?(a) 6.46 (b) 2.25 (c) 1.37 (d) 1.88Work Function =eV

Answered: The surface of a particular metal is…

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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I need some help with this.

The surface of a particular metal is initially exposed to light with a wavelength of X₁ = 350 nm and subsequently to
light with a wavelength of X₂ = 540 nm. It has been observed that the maximum speed of the emitted photoelectrons
differs by a factor of 2 between the two cases. The work function of the metal (in eV) can be approximated using
the formula:
1240
X
Which of the following values is closest to the work function of this metal?
(a) 6.46 (b) 2.25 (c) 1.37 (d) 1.88
Work Function =
eV

Expert Solution

Step 1: Relationship of maximum velocity of photon and work function:

From the photoelectric effect, we know:

$1 half m v subscript m a x end subscript superscript 2 equals fraction numerator h c over denominator lambda end fraction minus phi............ left parenthesis i right parenthesis W h e r e comma space m equals m a s s space o f space p h o t o n comma space v subscript m a x end subscript equals m a x i m u m space v e l o c i t y space o f space p h o t o n h equals P l a n k apostrophe s space c o n s tan t equals 6.626 cross times 10 to the power of negative 34 end exponent J. s c equals v e l o c i t y space o f space l i g h t equals 3.0 cross times 10 to the power of 8 space m s to the power of negative 1 end exponent lambda equals W a v e space l e n g t h space o f space l i g h t phi equals W o r k space f u n c t i o n space o f space m e t a l h e r e comma space v subscript m a x end subscript space i s space i n v e r e s l y space p r o p o r t i o n a l space t o space w a v e l e n g t h. S o comma space h e r e space g i v e n space lambda subscript 1 equals 350 space n m space a n d space lambda subscript 2 equals 540 space n m space left parenthesis h e r e comma 1 equals f i r s t space c o n d i t i o n space a n d space 2 equals s e c o n d space c o n d i t i o n right parenthesis S i n c e space h e r e space m a x i m u m space s p e e d space f o r space 1 s t space c o n d i t i o n space w i l l space b e space h i g h e r space t h a n space 2 n d space c o n d i t i o n. i. e. space space v subscript m a x end subscript subscript comma 1 end subscript over v subscript m a x end subscript subscript comma 2 end subscript equals 2$

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