Question

A container with 0.485 L of water is placed into microwave and is then radiated with electromagnetic energy that has a wavelength of 14.1 cm. The temperature of the water then rose by 69.9 °C. Calculate the number of photons that were absorbed by the water. Assume water has a density of 1.00 g·mL–1 and its specific heat is 4.184 J·g–1·°C–1

Answer 1

The number of photons that were absorbed by the water is about:

1.00 × 10²⁹ photons

$\texttt{ }$

Further explanation

The term of package of electromagnetic wave radiation energy was first introduced by Max Planck. He termed it with photons with the magnitude is:

$\large {\boxed {E = h \times f}}$

E = Energi of A Photon ( Joule )

h = Planck's Constant ( 6.63 × 10⁻³⁴ Js )

f = Frequency of Eletromagnetic Wave ( Hz )

$\texttt{ }$

The photoelectric effect is an effect in which electrons are released from the metal surface when illuminated by electromagnetic waves with large enough of radiation energy.

$\large {\boxed {E = \frac{1}{2}mv^2 + \Phi}}$

$\large {\boxed {E = qV + \Phi}}$

E = Energi of A Photon ( Joule )

m = Mass of an Electron ( kg )

v = Electron Release Speed ( m/s )

Ф = Work Function of Metal ( Joule )

q = Charge of an Electron ( Coulomb )

V = Stopping Potential ( Volt )

Let us now tackle the problem!

$\texttt{ }$

Given:

wavelength = λ = 14.1 cm

volume of water = V = 0.485 L

change in temperature = Δt = 69.9 °C

density of water = ρ = 1.00 g/mL = 1.00 kg/L

specific heat capacity of water = c = 4.184 J/g°C = 4184 J/kg°C

speed of light = c = 3 × 10⁸ m/s

Asked:

number of photons = N = ?

Solution:

$\texttt{ Heat absorbed by water } = \texttt{ Total Energy of Photons }$

$m c \Delta t = N h f$

$\rho V c \Delta t = N h \frac{c}{\lambda}$

$N = ( \rho V c \Delta t ) \div ( h \frac{c}{\lambda} )$

$N = ( 1.00 \times 0.485 \times 4184 \times 69.9 ) \div ( 6.63 \times 10^{-34} \times \frac{3 \times 10^8}{ 0.141 } )$

$N \approx 1.00 \times 10^{29} \texttt{ photons}$

$\texttt{ }$

Learn more

• Photoelectric Effect : brainly.com/question/1408276

• Statements about the Photoelectric Effect : brainly.com/question/9260704

• Rutherford model and Photoelecric Effect : brainly.com/question/1458544
• Photoelectric Threshold Wavelength : brainly.com/question/10015690

$\texttt{ }$

Answer details

Grade: High School

Subject: Physics

Chapter: Quantum Physics

Answer 2

Calculate the energy (J) increase due to heating. Then: Use energy per photon = h f = (Planck's constant)(frequency) frequency = (speed of light)/(wavelength) Divide: energy gain/energy per photon = number of photons