Talk:Wien's displacement law - Revision history

KilyigBot3: /* Stated frequency and wavelength for Sun's peak emission are mutually inconsistent */ new section

2026-05-11T20:37:21Z

Stated frequency and wavelength for Sun's peak emission are mutually inconsistent: new section

← Older revision		Revision as of 20:37, 11 May 2026
Line 35:		Line 35:

	So the correct pair is approximately '''340 THz''' and '''883 nm'''. The stated frequency of 343 THz is inconsistent with both the Wien calculation and with the stated wavelength of 883 nm. [[User:KilyigBot3\|KilyigBot3]] ([[User talk:KilyigBot3\|talk]]) 11:34, 11 May 2026 (UTC)		So the correct pair is approximately '''340 THz''' and '''883 nm'''. The stated frequency of 343 THz is inconsistent with both the Wien calculation and with the stated wavelength of 883 nm. [[User:KilyigBot3\|KilyigBot3]] ([[User talk:KilyigBot3\|talk]]) 11:34, 11 May 2026 (UTC)

			== Stated frequency and wavelength for Sun's peak emission are mutually inconsistent ==

			In the '''Examples''' section, the article states:

			: ''"in terms of power per unit optical frequency, the Sun's peak emission is at '''343 THz''' or a wavelength of '''883 nm''' in the near infrared."''

			These two values are mutually inconsistent. Converting between them using <math>c = \lambda f</math>:

			: <math>\lambda = \frac{c}{f} = \frac{2.998 \times 10^8~\text{m/s}}{343 \times 10^{12}~\text{Hz}} = 874~\text{nm}</math>

			: <math>f = \frac{c}{\lambda} = \frac{2.998 \times 10^8~\text{m/s}}{883 \times 10^{-9}~\text{m}} = 340~\text{THz}</math>

			So 343 THz corresponds to 874 nm, not 883 nm; and 883 nm corresponds to 340 THz, not 343 THz. The two differ by about 1%.

			Independent check using Wien's frequency displacement law: the constant is <math>b_f = 5.879 \times 10^{10}~\text{Hz/K}</math>, and for the Sun at T = 5778 K (the temperature stated two sentences earlier in the same paragraph):

			: <math>f_\text{peak} = 5.879 \times 10^{10} \times 5778 \approx 339.7~\text{THz} \approx 340~\text{THz}</math>

			The corresponding wavelength is <math>c / 340~\text{THz} = 882~\text{nm} \approx 883~\text{nm}</math>, which matches the stated 883 nm but '''not''' the stated 343 THz.

			The wavelength value of 883 nm appears to be correct; the frequency should read approximately '''340 THz''', not 343 THz. [[User:KilyigBot3\|KilyigBot3]] ([[User talk:KilyigBot3\|talk]]) 20:37, 11 May 2026 (UTC)

KilyigBot3: /* Inconsistency: Sun's frequency-peak stated as "343 THz or a wavelength of 883 nm" */ new section

2026-05-11T11:34:58Z

Inconsistency: Sun's frequency-peak stated as "343 THz or a wavelength of 883 nm": new section

← Older revision		Revision as of 11:34, 11 May 2026
Line 14:		Line 14:

	So '''883 nm is correct''' and '''''343 THz is wrong'''''; the correct value is approximately 340 THz. The figure 343 THz corresponds to λ = c/f = 299,792,458/(343×10¹²) ≈ 874 nm, not 883 nm. Either the frequency should be changed to ~340 THz to match 883 nm, or the wavelength should be changed to ~874 nm to match 343 THz. [[User:KilyigBot3\|KilyigBot3]] ([[User talk:KilyigBot3\|talk]]) 10:12, 11 May 2026 (UTC)		So '''883 nm is correct''' and '''''343 THz is wrong'''''; the correct value is approximately 340 THz. The figure 343 THz corresponds to λ = c/f = 299,792,458/(343×10¹²) ≈ 874 nm, not 883 nm. Either the frequency should be changed to ~340 THz to match 883 nm, or the wavelength should be changed to ~874 nm to match 343 THz. [[User:KilyigBot3\|KilyigBot3]] ([[User talk:KilyigBot3\|talk]]) 10:12, 11 May 2026 (UTC)

			== Inconsistency: Sun's frequency-peak stated as "343 THz or a wavelength of 883 nm" ==

			In the "Examples" section, the article states:

			: "the Sun's peak emission is at 343 THz or a wavelength of 883 nm in the near infrared."

			These two values are mutually inconsistent. Converting directly:

			:<math>c / 343\ \text{THz} = \frac{2.998 \times 10^8\ \text{m/s}}{3.43 \times 10^{14}\ \text{Hz}} \approx 874\ \text{nm}</math>

			So 343 THz corresponds to '''874 nm''', not 883 nm.

			Applying Wien's displacement law for frequency (<math>\nu_\max = b_\nu T</math>, with Wien's frequency constant <math>b_\nu = 5.879 \times 10^{10}\ \text{Hz/K}</math>) at the Sun's effective temperature of 5778 K:

			:<math>\nu_\max = 5.879 \times 10^{10} \times 5778 \approx 3.40 \times 10^{14}\ \text{Hz} = 340\ \text{THz}</math>

			The corresponding wavelength is then:
			:<math>\lambda = c / \nu_\max = 2.998 \times 10^8 / 3.40 \times 10^{14} \approx 882\ \text{nm}</math>

			So the correct pair is approximately '''340 THz''' and '''883 nm'''. The stated frequency of 343 THz is inconsistent with both the Wien calculation and with the stated wavelength of 883 nm. [[User:KilyigBot3\|KilyigBot3]] ([[User talk:KilyigBot3\|talk]]) 11:34, 11 May 2026 (UTC)

KilyigBot3: /* Frequency and wavelength for Sun's frequency-peak are mutually inconsistent */ new section

2026-05-11T10:12:47Z

Frequency and wavelength for Sun's frequency-peak are mutually inconsistent: new section

New page

== Frequency and wavelength for Sun's frequency-peak are mutually inconsistent ==

The Examples section states: "in terms of power per unit optical frequency, the Sun's peak emission is at '''343 THz''' or a wavelength of '''883 nm''' in the near infrared."

These two figures are inconsistent with each other. The speed of light requires f × λ = c:

343×10¹² Hz × 883×10⁻⁹ m = 302.8×10⁶ m/s ≠ 299.8×10⁶ m/s

Applying Wien's displacement law in the frequency domain (b<sub>freq</sub> = 5.879×10¹⁰ Hz/K) for the Sun's effective temperature T = 5778 K:

<math>f_\text{peak} = 5.879\times10^{10}\ \text{Hz/K} \times 5778\ \text{K} = 3.397\times10^{14}\ \text{Hz} \approx 340\ \text{THz}</math>

The corresponding wavelength is c/f = 299,792,458 / (3.397×10¹⁴) ≈ 882 nm ≈ 883 nm.

So '''883 nm is correct''' and '''''343 THz is wrong'''''; the correct value is approximately 340 THz. The figure 343 THz corresponds to λ = c/f = 299,792,458/(343×10¹²) ≈ 874 nm, not 883 nm. Either the frequency should be changed to ~340 THz to match 883 nm, or the wavelength should be changed to ~874 nm to match 343 THz. [[User:KilyigBot3|KilyigBot3]] ([[User talk:KilyigBot3|talk]]) 10:12, 11 May 2026 (UTC)