Question

Complete the table to determine if wavelength varies inversely with frequency. Let k be the product of wavelength and frequency.
Type of Radiation Wavelength (m) Frequency (1⁄sec) k
X–rays 1 × 10−10 3 × 1018 a
Radio waves 1 × 10−1 3 × 109 b
Green light 600 × 10−6 5 × 1011 c
UV rays 4 × 10−7 7.5 × 1014 d

Answer 1

The answers are
a= 3
b=3
c=3
d=3 

Answer 2

Answer:

For the X–rays is $a= 3\times 10^{8}$

For the Radio waves is $b= 3\times 10^{8}$

For the Green light is $c= 3\times 10^{8}$.

For the UV rays is $d= 3\times 10^{8}$.

Step-by-step explanation:

As given

k be the product of wavelength and frequency.

i.e

k = wavelength × frequency

First part

X–rays

$wavelength = 1\times 10^{-10}$

$frequency = 3\times 10^{18}$

Put in above equation

$k= 1\times 10^{-10}\times 3\times 10^{18}$

Now by using the exponent property

$x^{a}\times x^{b} = x^{a + b}$

$k= 3\times 10^{18-10}$

$k= 3\times 10^{8}$

i.e

$a= 3\times 10^{8}$

Thus for the X–rays is $a= 3\times 10^{8}$

Second part

For Radio waves .

$wavelength = 1\times 10^{-1}$

$frequency = 3\times 10^{9}$

Put in above equation

$k= 1\times 10^{-1}\times 3\times 10^{9}$

Now by using the exponent property

$x^{a}\times x^{b} = x^{a + b}$

$k= 3\times 10^{-1+9}$

$k= 3\times 10^{8}$

i.e

$b= 3\times 10^{8}$

Thus for the Radio waves is $b= 3\times 10^{8}$.

Third part

For Green light

$wavelength = 600\times 10^{-6}$

$frequency = 5\times 10^{11}$

Put in above equation

$k= 600\times 10^{-6}\times 5\times 10^{11}$

Now by using the exponent property

$x^{a}\times x^{b} = x^{a + b}$

$k= 3000\times 10^{-6+11}$

$k= 3\times 10^{5+3}$

$k= 3\times 10^{8}$

i.e

$c= 3\times 10^{8}$

Thus for the Green light is $c= 3\times 10^{8}$.

Fourth part

For UV rays

$wavelength = 4\times 10^{-7}$

$frequency = 7.5\times 10^{14}$

Put in above equation

$k= 4\times 10^{-7}\times 7.5\times 10^{14}$

Now by using the exponent property

$x^{a}\times x^{b} = x^{a + b}$

$k=30\times 10^{-7+14}$

$k= 30\times 10^{7}$

$k= 3\times 10^{7+1}$

$k= 3\times 10^{8}$

i.e

$d= 3\times 10^{8}$

Thus for the UV rays is $d= 3\times 10^{8}$.