Question
Determine the wavelength and frequency for light with energy of 257.9 kJ/mol.6.459 Xl014nM4.644 X1O-7
Determine the wavelength and frequency for light with energy of 257.9 kJ/mol. 6.459 Xl014 nM 4.644 X1O-7
Answers
Calculate the energy of a photon of blue light that has a wavelength of $450 \mathrm{nm}$
In this problem, we're told that we have light with an energy of 2112 kill a general's Permal and were asked to find the wavelength in nanometers. Associate it with this energy of light. We're furthermore, were asked, what portion of the electromagnetic spectrum this light falls into now. There are two key equations we need to solve this problem. First, we need Planck's equation, which tells us how the energy and the frequency of the slight is related to get to the wavelength. However, we also need to know how the frequency and the wavelength of related here c is the speed of light three times 10 to the eighth meters per second and H in this equation is Planck's constant, which is 6.626 times 10 to the negative. 34th jewels times seconds. However, there was one further problem plucks equation. Onley applies to a single photon, whereas were given the energy of an entire mole of photons. The first thing we need to do is convert this Moeller energy into the energy of one photon. To do this, we can use a dimensional analysis approach. We start with one photon of light, and we try to find how much energy it has. We know that in one mole of photons we will have of a God rose number or 6.2 times 10 to the 23rd photons. Furthermore, the problem statement told us that in every mole of photons we have 2112 killer jewels of energy. Now, we always like working in S I units. So we're going to convert this into jewels like so when we do this calculation, we find that one photon has approximately 3.507 times 10 to the negative 18th jewels of energy. That number we can use now. We can apply Planck's equation by rearranging we can solve for the frequency of this light and plug in our values. This is the value we just calculated above for a single photon energy content. And this is Planck's constant. When we put this in a calculator, we get a frequency of five 0.29 times 10 to the 15th for a second or hurts equivalent. The problem statement, however, asks us for wavelength. So now we can use our relationship between wavelength and frequency like so, rearrange it to solve for wavelength and plug in our values. In doing this, we get a wavelength of 5.67 times 10 to the negative eighth meters. Broaden State statement asked us to express this in nanometers. However, to do that we can multiply this value by 10 to the ninth because there are 10 to the ninth nanometers in 1 m and instead we find they have 56.7 nanometer wavelength. Okay, if you refer to a chart of the or electromagnetic spectrum, you will find that this lie squarely in the ultraviolet range.
Hi everyone. So in this question they asked calculate the energy in jewels of for dawn of green light having like 563. None of me that so thanks. We know that we know that is equal to let's see upon Lamba and 463 nm. That is equal to 463 In to tenders to -9 meter. So is equal to it's the upon limra That is equal to six 63 Into the national -34 jules again in two three into the next to eight mentor par second divided by 563 in 2, 10 national -9 m and therefore easy equal to three points. Mm is equal to three For you double three In to tenders to -19 June 10 Vegeta -19 Jule. Thanks Love.
Frequency is defined as C Upon prevalence. C is the speed of light and the wavelength of light is given 4 16 nanometer. So frequency of light, we will get 6.5 to 2. 10 to the power 14 huts. Yeah, they're excellent.
Good day. Even with the wavelet of a four ton of light, we can solve for the corresponding energy as E. It was Hc over lambda. Where E. Is the energy in jews, H is the planks constant, which is equal to 6.626 times 10 to the negative for jews. Second C is the speed of light, which is which value is three times 10 to the eight m per second. And lambda is the wavelengths of photons in meters. So given that a wavelength of a blue light is equal to 450 nm and we wish to find the energy corresponding to that Scotland are the energy that such photo and possesses. So we've met is 450 nm. And since we want the way that in terms of meters, so we will express nine millimeters, noting that one nanometer is equal to 10 to the negative nine of a meter. So that's 4 50 attempts sent to the negative name. So we have E equals H, which is 6.62, six times 10 to the negative 34 times three times 10 to the power of eight over 450 times 10 to the negative nine. So solving this one, using a calculator gives us the value in jewels for energy as 4.4. We're paying for two times 10 to the negative 19 juice. Hence this is the energy of a photon of a blue light. So I hope that is clear