Calculate the wavelength of a photon having energy of 1.257 X 10-24 joules. (Planck’s constant is 6.626 x 10-34 joule seconds;

Calculate the wavelength of a photon having energy of 1.257 X 10-24 joules. (Planck’s constant is 6.626 x 10-34 joule seconds; the speed of light is 2.998 x 108 m/s)
A.
5.10 m
B.
6.327 m
C.
0.324 m
D.
0.158 m

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Answer : The wavelength of a photon is, 3.6 m

Explanation :

$E=\frac{h\times c}{\lambda}$

where,

E = energy of photon = $5.518\times 10^{-26}J$

h = Planck's constant = $6.626\times 10^{-34}Js$

c = speed of light = $2.998\times 10^{8}m/s$

$\lambda$ = wavelength of a photon = ?

Now put all the given values in the above formula, we get the wavelength of a photon.

$5.518\times 10^{-26}J=\frac{6.626\times 10^{-34}Js\times 2.998\times 10^{8}m/s}{\lambda}$

$\lambda=3.599m\approx 3.6m$

Therefore, the wavelength of a photon is, 3.6 m

2. tonya3498 says:

The wavelength of the photon having twice the energy as that of the photon of wavelength $600\,{\text{nm}}$ is $\boxed{300\,{\text{nm}}}$ .

Further Explanation:

The photons are the small packets of energy that move at the speed of light. The photons are considered to remain always in motion. The energy associated with a moving photon is given by:

$E = \dfrac{{hc}}{\lambda }$

Here,  $E$  is the energy associated with the photon, $h$ is the Planck’s constant, $c$ is the speed of light and $\lambda$ is the wavelength of the moving photon.

The value of the Planck’s constant is $6.6 \times {10^{ - 34}}\,{\text{J}} \cdot {\text{s}}$ .

The wavelength of the photon is $600\,{\text{nm}}$ .

The energy associated with the photon of wavelength $600\,{\text{nm}}$ is:

\begin{aligned}{E_1}&=\frac{{\left( {6.6 \times {{10}^{ - 34}}} \right) \times \left( {3 \times {{10}^8}} \right)}}{{600 \times {{10}^{ - 9}}}}\\&=\frac{{1.98 \times {{10}^{ - 25}}}}{{6 \times {{10}^{ - 7}}}}\\&= 3.3 \times {10^{ - 19}}\,{\text{J}}\\\end{aligned}

The wavelength of photon having energy double of this:

\begin{aligned}E' &= 2{E_1}\\&= 2 \times\left( {3.3 \times {{10}^{ - 19}}} \right)\,{\text{J}}\\&{\text{ = 6}}{\text{.6}} \times {\text{1}}{{\text{0}}^{ - 19}}\,{\text{J}}\\\end{aligned}

The new wavelength of the photon will be:

$\lambda ' = \dfrac{{hc}}{{E'}}$

Substitute $6.6 \times {10^{ - 19}}\,{\text{J}}$ for $E'$ in above expression.

\begin{aligned}\lambda ' &= \frac{{\left( {6.6 \times {{10}^{ - 34}}} \right) \times \left( {3 \times {{10}^8}} \right)}}{{6.6 \times {{10}^{ - 19}}}}\\&=\frac{{1.98 \times {{10}^{ - 25}}}}{{6.6 \times {{10}^{ - 19}}}}\,{\text{m}}\\&= 3.0 \times {10^{ - 7}}\,{\text{m}}\\&= 300\,{\text{nm}}\\\end{aligned}

The wavelength of the photon having twice the energy as that of the photon of wavelength $600\,{\text{nm}}$ is $\boxed{300\,{\text{nm}}}$.

2.To find the number of neutrons in an atom you would

3.What is the frequency of light for which the wavelength is 7.1*10^2

Subject: Physics

Chapter: Photon and Energy

Keywords:  Wavelength, photon, energy, E=hc/lamda, 600nm, twice the energy, Planck’s constant, small packets of energy, 300nm, speed of light.

Planck's equation states that
E = hf
where
E =  the energy,
h = Planck's constant
f =  the frequency

Because
c = fλ
where
c =  velocity of light,
λ = wavelength
therefore
E = h(c/λ)

Photon 1:
The wavelength is λ₁ = 60 nm.
The energy is
E₁ = (hc)/λ₁

Photon 2:
The energy is twice that of photon 1, therefore its energy is
E₂ = 2E₁ = (hc)/λ₂.

Therefore
$\frac{E_{2}}{E_{1}}= \frac{(hc)/\lambda_{2}}{(hc)/60 \, nm} =2\\ \frac{60}{\lambda_{2}} =2 \\ \lambda_{2} = \frac{60}{2} =30 \, nm$

30 nm

4. eg12341 says:

For this equation you need to use the equation $E=h\frac{c}{λ}$

E is your Energy, h is Planck's constant, c is the speed of light and λ is wavelength

First re-arrange the equation to get λ by itself since that's what we are calculating

λ = h (c/E) plug in numbers
λ = 6.626 x10^-34Js [(2.998 x 10^8m/s)/1.257 x10^-24J)] evaluate
λ = 6.626 x10^-34 (2.385 x10^32)
λ ≈ 0.158 m

5. Tcareyoliver says:

The frequency of the $\lambda_2 = 622 nm = 622 \cdot 10^{-9} m$ wavelength photon is given by
$f_2 = \frac{c}{\lambda_2}= \frac{3 \cdot 10^8 m/s}{622 \cdot 10^{-9} m}=4.82 \cdot 10^{14} Hz$
where c is the speed of light.

The energy of this photon is
$E_2=hf_2 = (6.6 \cdot 10^{-34}Js)(4.82 \cdot 10^{14}Hz)=3.18 \cdot 10^{-19} J$
where h is the Planck constant.

The energy of the first photon is twice that of the second photon, so
$E_1 = 2 E_2 = 2 \cdot 3.18 \cdot 10^{-19}J =6.36 \cdot 10^{-19} J$

And so now by using again the relationship betwen energy and frequency, we can find the frequency of the first photon:
$f_1 = \frac{E_1}{h}= \frac{6.36 \cdot 10^{-19} J}{6.6 \cdot 10^{-34}Js}=9.64 \cdot 10^{14}Hz$

and its wavelength is
$\lambda_1 = \frac{c}{f_1}= \frac{3 \cdot 10^8 m/s}{9.64 \cdot 10^{14}Hz} =3.11 \cdot 10^{-7}m = 311 nm$
So, we see that the wavelength of the first photon is exactly half of the wavelength of the second photon (622 nm).

6. macyfrakes says:

The wavelength of a photon of energy 5.518 × 10-26 joules is 3.6 m. The energy of the photon is: E = h * f, where h is Planck's constant and f is the frequency. The frequency of the photon is: f = c/λ, where c is the speed of light and λ is the wavelength. Therefore: E = h * f = h * c / λ. We have that E = 5.518 × 10^-26 J; h = 6.626 × 10^-34 Js; c = 2.998 × 10^8 m/s. Substitute this in the formula for the energy of the photon: 5.518 × 10^-26 J = 6.626 × 10^-34 Js * 2.998 × 10^8 m/s / λ. 5.518 × 10^-26 J = 1.986 × 10^-25 Jm / λ. λ = 1.986 × 10^-25 Jm / 5.518 × 10^-26 J. λ = 0.36 × 10 m = 3.6 m.

7. chamillelynn says:

The wavelength of a photon of energy 5.518 × 10-26 joules is 3.6 m. The energy of the photon is: E = h * f, where h is Planck's constant and f is the frequency. The frequency of the photon is: f = c/λ, where c is the speed of light and λ is the wavelength. Therefore: E = h * f = h * c / λ. We have that E = 5.518 × 10^-26 J; h = 6.626 × 10^-34 Js; c = 2.998 × 10^8 m/s. Substitute this in the formula for the energy of the photon: 5.518 × 10^-26 J = 6.626 × 10^-34 Js * 2.998 × 10^8 m/s / λ. 5.518 × 10^-26 J = 1.986 × 10^-25 Jm / λ. λ = 1.986 × 10^-25 Jm / 5.518 × 10^-26 J. λ = 0.36 × 10 m = 3.6 m.

8. nakeytrag says:

1.096 i think

Explanation:

9. mauricioperez0902 says:

$E=h\nu\\\\&10;\nu=\frac{c}{\lambda} \ \ \ \Rightarrow E=\dfrac{hc}\lambda}\\\\&#10;\lambda=\dfrac{hc}{E}=\dfrac{6,626*10^{-34}Js*2,998*10^{8}\dfrac{m}{s}}{1,257*10^{-24}J}=15,803*10^{\frac{-34+8}{-24}}m=\\\\\\=15,803*10^{-2}m=1,5803*10^{-1}m$