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Show ALL equations, work, units, and significant figures in performing the following calculations. Identify the type of radiation in each problem. (Use your electromagnetic spectrum)
C = E = h
C = 3 . 0 0 x 1 0 8 m / s h = 6 . 6 2 6 2 x 1 0 - 3 4 J - s ( o r J / H z )
1 e V = 1 . 6 0 2 x 1 0 - 1 9 J
1 . W h a t i s t h e w a v e l e n g t h o f a w a v e h a v i n g a f r e q u e n c y o f 3 . 7 6 x 1 0 1 4 s - 1 ?
2 . W h a t i s t h e f r e q u e n c y o f a 6 . 9 x 1 0 - 1 3 m w a v e ?
3 . W h a t i s t h e w a v e l e n g t h o f a 2 . 9 9 H z w a v e ?
4 . W h a t i s t h e w a v e l e n g t h o f a 1 . 2 8 x 1 0 1 7 H z w a v e ?
5 . W h a t i s t h e f r e q u e n c y o f a 7 . 4 3 x 1 0 - 5 m w a v e ?
6 . W h a t i s t h e f r e q u e n c y o f a 2 , 6 0 0 c m w a v e ?
7 . W h a t i s t h e w a v e l e n g t h o f a 4 . 3 4 x 1 0 1 5 / s w a v e ?
8 . W h a t i s t h e f r e q u e n c y o f a 2 , 1 1 0 w a v e ?
9 . W h a t i s t h e f r e q u e n c y o f a 5 . 6 x 1 0 1 0 m w a v e ?
1 0 . W h a t i s t h e w a v e l e n g t h o f 1 0 9 . 6 M H z w a v e ?
1 1 . W h a t i s t h e e n e r g y o f a 7 . 6 6 x 1 0 1 4 H z w a v e ?
1 2 . W h a t i s t h e f r e q u e n c y o f a w a v e c a r r y i n g 8 . 3 5 x 1 0 - 1 8 J o f e n e r g y ?
1 3 . W h a t i s t h e f r e q u e n c y o f a 1 . 7 8 x 1 0 - 1 5 J w a v e ?
1 4 . W h a t i s t h e e n e r g y o f a 3 . 1 2 x 1 0 1 8 s - 1 w a v e ?
1 5 . W h a t i s t h e f r e q u e n c y o f a 1 . 3 1 x 1 0 - 2 2 J w a v e ? W h a t i s i t s w a v e l e n g t h ?
1 6 . W h a t i s t h e w a v e l e n g t h o f a 7 . 6 5 x 1 0 - 1 7 J w a v e ?
1 7 . W h a t i s t h e e n e r g y o f a 3 , 9 9 0 w a v e ?
1 8 . W h a t i s t h e e n e r g y o f a 9 , 3 3 0 c m w a v e ?
1 9 . W h a t i s t h e w a v e l e n g t h o f a 1 . 3 2 x 1 0 - 6 e V w a v e ?
2 0 . W h a t i s t h e e n e r g y i n e l e c t r o n - v o l t s ( e V ) o f a 4 . 2 2 m w a v e ?
2 1 . W h a t i s t h e w a v e l e n g t h o f a 1 . 5 2 8 x 1 0 - 1 3 J w a v e ?
C h e m i s t r y W o r k s h e e t W a v e l e n g t h , f r e q u e n c y , & e n e r g y o f e l e c t r o m a g n e t i c w a v e s . A N S W E R K E Y
S h o w A L L e q u a t i o n s , w o r k , u n i t s , a n d s i g n i f i c a n t f i g u r e s i n p e r f o r m i n g t h e f o l l o w i n g c a l c u l a t i o n s . I d e n t i f y t h e t y p e o f r a d i a t i o n i n e a c h p r o b l e m . ( U s e y o u r e l e c t r o m a g n e t i c s p e c t r u m )
C = E = h
C = 3 . 0 0 x 1 0 8 m / s h = 6 . 6 2 6 2 x 1 0 - 3 4 J - s ( o r J / H z )
e V = 1 . 6 0 2 x 1 0 - 1 9 J
W h a t i s t h e w a v e l e n g t h o f a w a v e h a v i n g a f r e q u e n c y o f
3 . 7 6 x 1 0 1 4 s - 1 ?
= c / = 3 . 0 0 x 1 0 8 m / s = 3 . 0 0 x 1 0 8 m x s = 7 . 9 8 x 1 0 - 7 m
3 . 7 6 x 1 0 1 4 s - 1 s 3 . 7 6 x 1 0 1 4
W h a t i s t h e f r e q u e n c y o f a 6 . 9 x 1 0 - 1 3 m w a v e ?
= c / = 3 . 0 0 x 1 0 8 m / s = 3 . 0 0 x 1 0 8 m x 1 = 4 . 3 5 x 1 0 2 0 s - 1
6 . 9 x 1 0 - 1 3 m s 6 . 9 x 1 0 - 1 3 m
3 . W h a t i s t h e w a v e l e n g t h o f a 2 . 9 9 H z w a v e ?
= c / = 3 . 0 0 x 1 0 8 m / s x 1 H z = 3 . 0 0 x 1 0 8 m x s = 1 . 0 0 x 1 0 8 m
2 . 9 9 H z s - 1 s 2 . 9 9
4 . W h a t i s t h e w a v e l e n g t h o f a 1 . 2 8 x 1 0 1 7 H z w a v e ?
= c / = 3 . 0 0 x 1 0 8 m/s = 1 Hz x 3.00 x 108 m x s________
1.28 x 1017 Hz s-1 s 1.28 x 1017
= 2.34 x 10-9 m
5. What is the frequency of a 7.43 x 10-5 m wave?
6. What is the frequency of a 2,600 cm wave?
7. What is the wavelength of a 4.34 x 1015 /s wave?
8 . W h a t i s t h e f r e q u e n c y o f a 2 , 1 1 0 w a v e ?
= c / = 3 . 0 0 x 1 0 8 m / s = 3 . 0 0 x 1 0 8 m x 1 x 1 = 1 . 4 2 x 1 0 1 5 s - 1
2 , 1 1 0 s 2 , 1 1 0 1 0 - 1 0 m
9 . W h a t i s t h e f r e q u e n c y o f a 5 . 6 x 1 0 1 0 m w a v e ?
= c / = 3 . 0 0 x 1 0 8 m / s = 3 . 0 0 x 1 0 8 m x 1 x 1 m = 5 . 4 x 1 0 3 s -
5 . 6 x 1 0 1 0 m s 5 . 6 x 1 0 1 0 m 1 0 - 6 m
1 0 . W h a t i s t h e w a v e l e n g t h o f 1 0 9 . 6 M H z w a v e ?
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1 1 . W h a t i s t h e e n e r g y o f a 7 . 6 6 x 1 0 1 4 H z w a v e ?
E = h = 6 . 6 2 6 2 x 1 0 - 3 4 J / H z x 7 . 6 6 x 1 0 1 4 H z = 5 . 0 7 x 1 0 - 1 9 J
1 2 . W h a t i s t h e f r e q u e n c y o f a w a v e c a r r y i n g 8 . 3 5 x 1 0 - 1 8 J o f e n e r g y ?
= E / h = 8 . 3 5 x 1 0 - 1 8 J = 1 . 2 6 x 1 0 1 6 s - 1
6 . 6 2 6 2 x 1 0 - 3 4 J - s
1 3 . W h a t i s t h e f r e q u e n c y o f a 1 . 7 8 x 1 0 - 1 5 J w a v e ?
= E / h = 1 . 7 8 x 1 0 - 1 5 J = 2 . 6 9 x 1 0 1 8 s - 1
6 . 6 2 6 2 x 1 0 - 3 4 J - s
1 4 . W h a t i s t h e e n e r g y o f a 3 . 1 2 x 1 0 1 8 s - 1 w a v e ?
E = h = 6 . 6 2 6 2 x 1 0 - 3 4 J - s x 3 . 1 2 x 1 0 1 8 s -
= 2 . 0 7 x 1 0 - 1 5 J
1 5 . W h a t i s t h e f r e q u e n c y o f a 1 . 3 1 x 1 0 - 2 2 J w a v e ? W h a t i s i t s w a v e l e n g t h ?
= E / h = 1 . 3 1 x 1 0 - 2 2 J = 1 . 9 7 7 0 0 0 3 9 2 x 1 0 1 1 s - 1 = 1 . 9 8 x 1 0 + 1 1 s - 1
6 . 6 2 6 2 x 1 0 - 3 4 J - s
= c / = 3 . 0 0 x 1 0 8 m / s
1 . 9 7 7 0 0 0 3 9 2 x 1 0 1 1 s - 1
= 3 . 0 0 x 1 0 8 m x s = 0 . 0 0 1 5 2 m = 1 . 5 2 x 1 0 - 3 m
s 1 . 9 7 7 0 0 0 3 9 2 x 1 0 1 1
1 6 . W h a t i s t h e w a v e l e n g t h o f a 7 . 6 5 x 1 0 - 1 7 J w a v e ?
= E / h = 7 . 6 5 x 1 0 - 1 7 J = 1 . 1 5 4 5 0 7 8 6 3 x 1 0 1 7 s - 1
6 . 6 2 6 2 x 1 0 - 3 4 J - s
= c / = 3 . 0 0 x 1 0 8 m / s =
1 . 1 5 4 5 0 7 8 6 3 x 1 0 1 7 s - 1
= 3 . 0 0 x 1 0 8 m x s = 0 . 0 0 1 5 2 m = 1 . 5 2 x 1 0 - 3 m
s 1 . 1 5 4 5 0 7 8 6 3 x 1 0 1 7
1 7 . W h a t i s t h e e n e r g y o f a 3 , 9 9 0 w a v e ?
= c / = 3 . 0 0 x 1 0 8 m / s = 3 . 0 0 x 1 0 8 m x 1 x 1 =
3 , 9 9 0 s 3 , 9 9 0 1 0 - 1 0 m
= 7 . 5 1 8 7 9 6 9 9 2 x 1 0 1 3 s -
E = h = 6 . 6 2 6 2 x 1 0 - 3 4 J - s x 7 . 5 1 8 7 9 6 9 9 2 x 1 0 1 3 s -
= 4 . 9 8 x 1 0 - 1 9 J
1 8 . W h a t i s t h e e n e r g y o f a 9 , 3 3 0 c m w a v e ?
= c / = 3 . 0 0 x 1 0 8 m / s = 3 . 0 0 x 1 0 8 m x 1 x 1 c m = 3 . 2 1 5 4 3 4 0 8 4 x 1 0 6 s - 1
9 , 3 3 0 c m s 9 , 3 3 0 c m 1 0 - 2 m
E = h = 6 . 6 2 6 2 x 1 0 - 3 4 J - s x 3 . 2 1 5 4 3 4 0 8 4 x 1 0 6 s - 1 = 2 . 1 3 x 1 0 - 2 7 J
1 9 . W h a t i s t h e w a v e l e n g t h o f a 1 . 3 2 x 1 0 - 6 e V w a v e ?
= E / h = 1 . 3 2 x 1 0 - 6 e V x 1 . 6 0 2 x 1 0 - 1 9 J = 3 . 1 9 1 3 3 1 3 8 x 1 0 + 8 s - 1
6 . 6 2 6 2 x 1 0 - 3 4 J - s 1 e V
= c / = 3 . 0 0 x 1 0 8 m / s = 3 . 0 0 x 1 0 8 m x 1
3 . 1 9 1 3 3 1 3 8 x 1 0 + 8 s - 1 s 3 . 1 9 1 3 3 1 3 8 x 1 0 + 8 s - 1
= 0 . 9 4 0 m
2 0 . W h a t i s t h e e n e r g y i n e l e c t r o n - v o l t s ( e V ) o f a 4 . 2 2 m w a v e ?
= c / = 3 . 0 0 x 1 0 8 m / s = 3 . 0 0 x 1 0 8 m x 1 x 1 m
4 . 2 2 m s 4 . 2 2 m 1 0 - 6 m
= 7 . 1 0 9 0 0 4 7 3 x 1 0 1 3 s -
E = h = 6 . 6 2 6 2 x 1 0 - 3 4 J - s x = 7 . 1 0 9 0 0 4 7 3 x 1 0 1 3 s - = 4 . 7 1 x 1 0 - 2 0 J
2 1 . W h a t i s t h e w a v e l e n g t h o f a 1 . 5 2 8 x 1 0 - 1 3 J w a v e ?
= E / h = 1 . 5 2 8 x 1 0 - 1 3 J = 2 . 3 0 5 9 9 7 4 0 4 x 1 0 2 0 s - 1
6 . 6 2 6 2 x 1 0 - 3 4 J - s
= c / = 3 . 0 0 x 1 0 8 m / s = 3 . 0 0 x 1 0 8 m x 1 _ _ _ _ _ _ _ _ _ _ _
2 . 3 0 5 9 9 7 4 0 4 x 1 0 2 0 s - 1 s 2 . 3 0 5 9 9 7 4 0 4 x 1 0 2 0 s - 1
= 1 . 3 0 x 1 0 - 1 2 m
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