Question

(a) What is the intensity in W/m2 of a laser beam used to burn away cancerous tissue that, when 90.0% absorbed, puts 500 J of energy into a circular spot 2.00 mm in diameter in 4.00 s

Answer 1

Answer:

4.42 x 10⁷ W/m²

Explanation:

A = energy absorbed = 500 J

η = efficiency = 0.90

E = Total energy

Total energy is given as

E = A/η

E = 500/0.90

E = 555.55 J

t = time = 4.00 s

Power of the beam is given as

P = E /t

P = 555.55/4.00

P = 138.88 Watt

d = diameter of the circular spot = 2.00 mm = 2 x 10⁻³ m

Area of the circular spot is given as

A = (0.25) πd²

A = (0.25) (3.14) (2 x 10⁻³)²

A = 3.14 x 10⁻⁶ m²

Intensity of the beam is given as

I = P /A

I = 138.88 / (3.14 x 10⁻⁶)

I = 4.42 x 10⁷ W/m²

Answer 2

The intensity of a laser beam : 4.42.10⁷ W/m²

Further explanation

The energy transferred by waves per unit area per unit time is called wave intensity  

Because energy per unit time is Power, the intensity of the wave is equal to Power divided by area  

$\rm P=\dfrac{W}{t}$

P = power, watt

W = energy, J  

t = time, s  

For waves that spread in all directions, the intensity at the distance R from the source can be formulated  

$\rm I=\dfrac{Power}{Area}=\dfrac{P}{\pi .R^2}$

From the equation above shows the intensity of the wave is inversely proportional to the square of the distance from the source.  

$\rm I\approx \dfrac{1}{R^2}$

The farther the wave spreads, the smaller the intensity  

Cancerous tissue area:

$\rm A=\dfrac{1}{4}\pi d^2\\\\A=\dfrac{1}{4}\pi(2.10^{-3})^2\Rightarrow d=2~mm=2.10^{-3}\:m\\\\A=\frac{1}{4}\pi 4.10^{-6}\\\\A=\pi .10^{-6}\\\\A=3.14.10^{-6}$

So that the intensity

$\rm 0.9I(only~90\%~absorbed)=\dfrac{W}{A.t}\\\\0.9I=\dfrac{500}{3.14.10^{-6}.4}\\\\I=4.42.10^7~\dfrac{W}{m^2}$

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