Question

How do I fill the following table?

Use 3 significant figures and the accepted prefixes (kilo, mega, giga, tera, mili, micro, nano, etc.)

EM-WAVE RANGE (colour)	Wavelength	Frequency (Hz)	Energy (eV)	Temperature (K)
Long radio waves	1 km
	21 cm
				2.7 K
	5 cm
	0.1 mm
	0.01 mm
				36.7 C
	750 nm
Red	660 nm
	550 nm
	400 nm
	380 nm
	300 nm
	200 nm
	10 nm
	0.1 nm
	1 pm
	1 fm
				10^7 K

Answer 1

To fill the blank spaces, use following relations:

E : Energy : Unit: Joules (J)

f = frequency : Unit : Hertz (Hz)

l = wavelength : Unit : meter (m)

T = temperature: Unit : Kelvin (K)

1. E = h*f

Where, h is planck's constant = 6.63 * 10^-34 m² kg/s

2. f * l = c

frequency * wavelength = speed of light

c: speed of light = 3 * 10⁸ m/s

3. l = b/T (Wein's displacement law)

b: wein's displacement constant = 2.9 * 10^-3 m K

Using any of the above three relations you can find the required values of l, f , E or T if any one is given.

1. Take the 1st row:

l = 1 km = 10³ m

a) Thus, to find f, use l * f = c:

10³ * f = 3 * 10⁸

or,

f = 3 * 10⁸ /10³ = 3 * 10⁵ Hz

b) To find E, use: E = h*f

E = 6.63 * 10^-34 * 3 * 10⁵ = 1.99 * 10^-29 J

c) To find T, use: l = b/T

or, T = b / l = 2.9 * 10^-3 / 1 = 2.9 * 10^-3 K

Similarily we can find others:

2. l = 21 cm = 0.21 m

Thus, f = 3 * 10⁸ / 0.21 = 1.43 * 10⁹ Hz

E = 6.63 * 10^-34 * 1.43 * 10⁹ = 9.47 * 10^-25 J

T = 2.9 * 10^-3 / 0.21 = 1.38 * 10^-2 K

3.

Here T = 2.7 K is given.

So we 1st find l:

l = b / T = 2.9 * 10^-3 / 2.7 = 1.1 * 10^-3 m

f = 3 * 10⁸ / (1.1 * 10^-3 ) = 2.73 * 10¹¹ Hz

E = 6.63 * 10^-34 * 2.73 * 10¹¹ = 1.81 * 10^-22 J

Similarily as shown above you can fill rest of the blanks

NOTE:

For T = 36.7 C, you have to convert 1st to Kelvin: T (K) = 274.15 + T (C)

So, 36.7 C = 274.15 +36.7 = 309.85 K