91Ó°ÊÓ

Speed of electromagnetic wave,$c=3.00×{10}^{8}m/s$

Wavelength of visible${\mathrm{λ}}_1=400nmor400×{10}^{-9}m$

Wavelength of visible light${\mathrm{λ}}_2=700nmor700×{10}^{-9}m$

Frequency ranges,$f=1.5to300MHz$

X ray wavelength range is $5.0nmor1.0×{10}^{-2}nm$

Here we have to use the basic formula for wave velocity in terms of wavelength and frequency.

Formula:

The speed of light, $c=f\mathrm{λ}....…\left(1\right)$

Using equation (1), we get the value of maximum frequency of visible light for first wavelength as:

$$\begin{gathered} f_1=\frac{v}{{\mathrm{λ}}_1} \\ =\frac{3.00×{10}^8}{400×{10}^{-9}} \\ =7.5×{10}^{14}Hz \end{gathered}$$

Now minimum frequency$f_2$using equation (1) is given as follows:

localid="1660992239723" $$\begin{gathered} f_2=\frac{v}{{\mathrm{λ}}_2} \\ =\frac{3.00×{10}^8}{700×{10}^{-9}} \\ =4.3×{10}^{14}Hz \end{gathered}$$.

Hence, the range of frequencies is $4.3×{10}^{14}Hzand7.5×{10}^{14}Hz$

Now using minimum frequency and equation (1), we get the wavelength${\mathrm{λ}}_1$as:

$\begin{array}{l}{\mathrm{λ}}_1=\frac{3.00×{10}^8}{300×{10}^6}\\ =1.0m\end{array}$.

Now using maximum frequency and equation (1), we get the wavelength${\mathrm{λ}}_2$as:

$\begin{array}{l}{\mathrm{λ}}_2=\frac{3.00×{10}^8}{1.5×{10}^6}\\ =200m\end{array}$

Hence, the value of wavelength range is $1.0\mathrm{m}\mathrm{and}2.0×{10}^2\mathrm{m}$

Now minimum frequency$f_1$using equation (1) for x-rays is given as:

$\begin{array}{l}{f}_1=\frac{3.00×{10}^8}{5×{10}^{-9}}\\ =6.0×{10}^{16}Hz\end{array}$

Now maximum frequency$f_2$using equation (1) for x-rays is given as:

$\begin{array}{l}{f}_2=\frac{3.00×{10}^8}{1.0×{10}^{-11}}\\ =3.0×{10}^{19}Hz\end{array}$

Hence, the value of frequency range for x rays is$6.0×{10}^{16}Hzand3.0×{10}^{19}Hz$