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k0ka [10]
2 years ago
5

Pulsed dye lasers emit light of wavelength 585 nm in 0.45 ms pulses to remove skin blemishes such as birthmarks. The beam is usu

ally focused onto a circular spot 3.4 mm in diameter. Suppose that the output of one such laser is 20.0 W .(a) What is the energy of each photon, in eV? (b) How many photons per square millimeter are delivered to the blemish during each pulse?
Physics
1 answer:
koban [17]2 years ago
8 0

Answer:

a) E₀ = 2.125 eV, b)     # photon2 = 9.2 10¹⁵ photons / mm²

Explanation:

a) To calculate the energy of a photon we use Planck's education

      E = h f

And the ratio of the speed of light

     c = λ f

We replace

      E = h c /λ

Let's calculate

      E₀ = 6.63 10⁻³⁴ 3 10⁸/585 10⁻⁹

      E₀ = 3.40 10⁻¹⁹ J

Let's reduce

     E₀ = 3.4 10⁻¹⁹ J (1 eV / 1.6 10⁻¹⁹ J)

     E₀ = 2.125 eV

b) Let's look for the energy in each pulse

       P = E / t

       E = P t

       E = 20.0 0.45 10⁻³

       E = 9 10⁻³ J

let's use a ratio of proportions (rule of three) if we have the energy of a photon (E₀), to have the energy of 9 10⁻³ J

       # photon = 9 10⁻³ /3.40 10⁻¹⁹

      # photon = 2.65 10¹⁶ photons

Let's calculate the areas

Focus area

      A₁ = π r²

     A₁ = π (3.4/2)²

     A₁ = 9,079 mm²2

Area requested for calculation r = 1 mm

     A₂ = π 1²

     A₂ = 3.1459 mm²

 

Let's use another rule of three. If we have 2.65 106 photons in an area A1 how many photons in an area A2

    # photon2 = 2.65 10¹⁶ 3.1459 / 9.079

   # photon2 = 9.2 10¹⁵ photons / mm²

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Lelechka [254]

Answer:

a) T = 6.49*10^-3 s

b) v = 8 m/s

c) E = 3 J

d) F = 733 N

e) F = 366.5 J

Explanation:

Given

Mass of particle, m = 94 g = 0.094 kg

Amplitude of the particle, A = 8.3 mm = 8.3*10^-3 m

Maximum acceleration of particle, a = 7.8*10^3 m/s²

the equation describing Simple Harmonic Motion is given as

x = A cos (wt +φ)

To fond the acceleration of this relationship, we would have to integrate. Twice, the first would be a Velocity, and the second acceleration that we need.

Velocity = dx/dt = -Aw sin(wt + φ)

Acceleration = d²x/dt = -Aw² cos(wt + φ)

From the question, we were given, magnitude of acceleration to be 7.8*10^3 m/s²

Aw² = 7.8*10^3

w² = 7.8*10^3 / A

w² = 7.8*10^3 / 8.3*10^-3

w² = 939759

w = √939759

w = 969

Recall, T = 2π/w, so that

T = (2 * 3.142) / 969

T = 6.49*10^-3 s

Maximum speed = Aw

Maximum speed = 8.3*10^-3 * 969

Maximum speed = 8.0 m/s

Total mechanical energy oscillator =

mgx + 1/2mx² =

1/2mv(max)² =

1/2 * 0.094 * 8² =

3 J

Maximum displacement

x = A cos(wt + φ)

For x to be maximum here, then cos(wt + φ) Must be equal to 1

Acceleration = d²x/dt² = -Aw²

And force = mass * acceleration

Force = 0.094 * 7.8*10^3

Force = 733 N

x = A cos(wt + φ), where cos(wt + φ) = 1/2

d²x/dt² = -Aw² * 1/2

d²x/dt² = 733 * 0.5

= 366.5 N

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Carbon atoms can form straight, and branched chains, and rings
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3 years ago
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musickatia [10]

Answer:

1. False

2. Fats

3. False

Explanation:

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3 years ago
What minimum speed does a 200 g puck need to make it to the top of a frictionless ramp that is 4.1 m long and inclined at 22 ∘?
myrzilka [38]

Answer:

5.5 m/ sec

Explanation:

Because the inclined surface is frictionless so we can assume that total change of energy is zero

i-e ΔE = 0

Or we can say that difference between final and initial energy is zero i-e

Ef- Ei =0

Where,

Ef= final energy at the top of the ramp= KEf+PEf

Ei= Initial energy at the bottom of the ramp=KEi+PEi

So we have

(KEf+PEf)-(KEi+PEi)=0

==>KEf-KEi+PEf-PEi=0            -------------(1)

KEf = mgh = 200×9.8×h

Where h= Sin 22 = h/d= h/4.1

or

0.375×4.1=h

or h= 1.54 m

So, PEf= 200×9.8×1.54=3018.4 j

and KEf= 1/2 mVf^{2}= 0.5×200×0=0 j

PEi= mgh = 200×9.8×0=0 j

KEi= 1/2 mVi^{2}=0.5×200×Vi^{2}=100Vi^{2} j

Put these values in eq 1, we get;

0-100 Vi^{2}+3018.4-0=0

-100 Vi^{2}=-3018.4

==> Vi^{2}= \frac{3018.4}{100} = 30.184

==>  Vi = \sqrt{30.184}  = 5.5 m.sec

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3 years ago
The position x, in meters, of an object is given by the equation:
LenaWriter [7]

Answer:

The SI units of A, B and C are :

m,\ m/s\ and\ m/s^2                  

Explanation:

The position x, in meters, of an object is given by the equation:

x=A+Bt+Ct^2

Where

t is time in seconds

We know that the unit of x is meters, such that the units of A, Bt and Ct^2 must be meters. So,

  • A=m
  • bt=m

b=\dfrac{m}{s}=m/s

  • Ct^2=m

C=m/s^2

So, the SI units of A, B and C are :

m,\ m/s\ and\ m/s^2

So, the correct option is (B).

3 0
3 years ago
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