Ch.6 - Electronic Structure of Atoms

Problem 32

Chapter 6, Problem 32

A stellar object is emitting radiation at 3.0 mm. (a) What type of electromagnetic spectrum is this radiation (b) If a detector is capturing 3.0 3 108 photons per second at this wavelength, what is the total energy of the photons detected in 1 day?

Verified step by step guidance

Step 1: Identify the type of electromagnetic radiation. The wavelength of the radiation is given as 3.0 mm. This falls within the range of the microwave region of the electromagnetic spectrum. Therefore, the radiation is a microwave radiation.

Step 2: Calculate the energy of a single photon. The energy of a photon can be calculated using the formula E = h*c/λ, where E is the energy, h is Planck's constant (6.626 x 10^-34 J*s), c is the speed of light (3.0 x 10^8 m/s), and λ is the wavelength. Remember to convert the wavelength from mm to m before using it in the formula.

Step 3: Calculate the energy of all photons detected per second. Multiply the energy of a single photon by the number of photons detected per second (3.0 x 10^8 photons/second).

Step 4: Calculate the total energy of photons detected in 1 day. There are 86400 seconds in a day. Multiply the energy of all photons detected per second by the number of seconds in a day to get the total energy of photons detected in 1 day.

Step 5: The result from step 4 is the total energy of the photons detected in 1 day. Remember to express your answer in the correct units of energy (Joules).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, which vary in wavelength and frequency. Radiation at 3.0 mm falls within the microwave region of the spectrum, which is used in various applications, including communication and cooking. Understanding the position of radiation within the spectrum helps in identifying its properties and potential uses.

Photon Energy

Photons are particles of light, and their energy is directly related to their frequency, as described by the equation E = hν, where E is energy, h is Planck's constant, and ν is frequency. For radiation at 3.0 mm, calculating the energy of individual photons requires converting the wavelength to frequency using the speed of light. This concept is crucial for determining the total energy of multiple photons.

Energy Calculation Over Time

To find the total energy of photons detected over a specific time period, one must multiply the energy of a single photon by the number of photons detected and the duration of detection. In this case, if 3.0 x 10^8 photons are captured per second, the total energy over one day (86,400 seconds) can be calculated by integrating these values. This concept is essential for understanding how energy accumulates from continuous photon detection.

Recommended video:

Guided course

01:29

The Gibbs Free Energy Formula Example

Related Practice

Textbook Question

One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 325 nm. (d) These UV photons can break chemical bonds in your skin to cause sunburn—a form of radiation damage. If the 325-nm radiation provides exactly the energy to break an average chemical bond in the skin, estimate the average energy of these bonds in kJ/mol.

views

Textbook Question

The energy from radiation can be used to rupture chemical bonds. A minimum energy of 192 kJ/mol is required to break the bromine–bromine bond in Br2. What is the longest wavelength of radiation that possesses the necessary energy to break the bond? What type of electromagnetic radiation is this?

views

Textbook Question

A diode laser emits at a wavelength of 987 nm. (a) In what portion of the electromagnetic spectrum is this radiation found? (b) All of its output energy is absorbed in a detector that measures a total energy of 0.52 J over a period of 32 s. How many photons per second are being emitted by the laser?

views

Textbook Question

Molybdenum metal must absorb radiation with an energy higher than 7.22 * 10-19 J ('energy threshold') before it can eject an electron from its surface via the photoelectric effect. (a) What is the frequency threshold for emission of electrons?

views

Textbook Question

Molybdenum metal must absorb radiation with an energy higher than 7.22 * 10-19 J ('energy threshold') before it can eject an electron from its surface via the photoelectric effect. (b) What wavelength of radiation will provide a photon of this energy?

views

Textbook Question

Molybdenum metal must absorb radiation with an energy higher than 7.22 * 10-19 J ('energy threshold') before it can eject an electron from its surface via the photoelectric effect. (c) If molybdenum is irradiated with light of wavelength of 240 nm, what is the maximum possible velocity of the emitted electrons?