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(i)The number of electrons per second striking the target (ii)The velocity of the incident electrons .

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Hint: X- ray is a light but it has more power and energy than light detected by our eyes. If electrons will strike at X ray or any other ray then some amount of electron which the electron has is transferred to the X- ray and untransfered energy will remain as an electron. To calculate energy use a simple formula of kinetic energy which must be equal to electron volt. Use the formula of power.

Complete step by step answer:

Potential difference is given by 40kV operated on X-ray tubes.

And heat produced is 720W

0.5 % of the energy of the incident electron is converted into X- ray. Then the remaining energy the electron has is 99.5% i.e. 0.995. it means 99.5% remain from total power.

Mathematically, power is given by,

P = 0.995 VI

Therefore,

$I=\dfrac{P}{0.995\times V}$

Put values of power i.e 720W and potential difference (p) is 40Kv in above equations,

We get,

$\begin{align}

& I=\dfrac{720}{0.995\times 40\times {{10}^{3}}} \\

& I=0.018 \\

\end{align}$

(i) The number of electron per second striking the target

Number of electrons is given by,

$\begin{align}

& Number\text{ }of\text{ }electrons\text{ }=\dfrac{current}{charge on electron} \\

& n=\dfrac{I}{q} \\

& n=\dfrac{0.018}{1.6\times {{10}^{-19}}} \\

& n=1.1\times {{10}^{17}}electrons \\

\end{align}$

The number of electron per second striking the target $n=1.1\times {{10}^{17}}electrons$

(ii)The velocity of the incident electrons.

Energy of incident electron is given by,

Use formula of kinetic energy then,

\[\begin{align}

& \dfrac{1}{2}m{{v}^{2}}=eV \\

& V=\sqrt{\dfrac{2eV}{m}} \\

& V=\sqrt{{{\dfrac{2\times 1.6\times 40\times {{10}^{3}}\times 10}{9.1\times {{10}^{-31}}}}^{-19}}}m/\sec \\

& V=1.2\times {{10}^{8}}m/\sec \\

\end{align}\]

The velocity of the incident electrons is \[V=1.2\times {{10}^{8}}m/\sec \].

Note: First understand what the question wants to convey then try to analyse the solution. X-ray are electromagnetic waves of very short wavelength. Use a direct formula of energy. Number of electrons is equal to the current by charge of the electron. Use a formula of power which is equal to the product of voltage and current.

Complete step by step answer:

Potential difference is given by 40kV operated on X-ray tubes.

And heat produced is 720W

0.5 % of the energy of the incident electron is converted into X- ray. Then the remaining energy the electron has is 99.5% i.e. 0.995. it means 99.5% remain from total power.

Mathematically, power is given by,

P = 0.995 VI

Therefore,

$I=\dfrac{P}{0.995\times V}$

Put values of power i.e 720W and potential difference (p) is 40Kv in above equations,

We get,

$\begin{align}

& I=\dfrac{720}{0.995\times 40\times {{10}^{3}}} \\

& I=0.018 \\

\end{align}$

(i) The number of electron per second striking the target

Number of electrons is given by,

$\begin{align}

& Number\text{ }of\text{ }electrons\text{ }=\dfrac{current}{charge on electron} \\

& n=\dfrac{I}{q} \\

& n=\dfrac{0.018}{1.6\times {{10}^{-19}}} \\

& n=1.1\times {{10}^{17}}electrons \\

\end{align}$

The number of electron per second striking the target $n=1.1\times {{10}^{17}}electrons$

(ii)The velocity of the incident electrons.

Energy of incident electron is given by,

Use formula of kinetic energy then,

\[\begin{align}

& \dfrac{1}{2}m{{v}^{2}}=eV \\

& V=\sqrt{\dfrac{2eV}{m}} \\

& V=\sqrt{{{\dfrac{2\times 1.6\times 40\times {{10}^{3}}\times 10}{9.1\times {{10}^{-31}}}}^{-19}}}m/\sec \\

& V=1.2\times {{10}^{8}}m/\sec \\

\end{align}\]

The velocity of the incident electrons is \[V=1.2\times {{10}^{8}}m/\sec \].

Note: First understand what the question wants to convey then try to analyse the solution. X-ray are electromagnetic waves of very short wavelength. Use a direct formula of energy. Number of electrons is equal to the current by charge of the electron. Use a formula of power which is equal to the product of voltage and current.

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