On This Day — US Detonates First Nuclear Weapon (Trinity Test, July 16, 1945) | The Magical World of Dimensional Analysis

“We knew the world would not be the same. A few people laughed, a few people cried. Most people were silent. I remembered the line from the Hindu scripture, the Bhagavad Gita. ‘Now I am become Death, the destroyer of worlds.’ I suppose we all thought that, one way or another.”

J. Robert Oppenheimer

The Trinity Test, July 16, 1945. Captured 25 milliseconds after detonation, this image shows the expanding fireball, which had reached a diameter of approximately 140 metres. (Photograph published by Life magazine.)

July 15, 2026 — On July 16, 1945, the US detonated the world’s first nuclear weapon, a plutonium-based device, near Alamogordo, New Mexico. Trinity, as the test was known, was successful. Three weeks later, the United States used an atomic bomb against the Japanese city of Hiroshima, marking the first wartime use of a nuclear weapon. The world would never be the same. Follow us on Twitter: @INTEL_TODAY

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An estimated 80,000 of Hiroshima’s 350,000 people were killed instantly. By the end of the year, the death toll would rise to 140,000 as survivors succumbed to injuries or radiation illnesses.

Trinity was the code name for the first detonation of a nuclear weapon. Conducted by the United States Army at 5:29 a.m. on July 16, 1945, it was the first major test of the Manhattan Project.

The test took place in the Jornada del Muerto desert, about 35 miles (56 km) southeast of Socorro, New Mexico, at what was then the USAAF Alamogordo Bombing and Gunnery Range.

The device tested was an implosion-design plutonium weapon, informally known as “The Gadget.” Its design was essentially the same as that of the Fat Man bomb later detonated over Nagasaki, Japan, on August 9, 1945.

The Trinity detonation released energy equivalent to approximately 22 kilotons of TNT — about 92 terajoules (TJ) — marking the beginning of the nuclear age.

Real vs. Reel — Test mannequins used to study the effects of an atomic bomb during atmospheric nuclear tests in the Nevada desert. Left: a photograph published by LIFE magazine. The unburned mannequin, with her wig slightly askew, wears a light-colored dress designed to study the effects of thermal radiation and heat absorption. Right: a scene from Indiana Jones and the Kingdom of the Crystal Skull illustrating a fictional depiction of an atomic blast.

The Magical World of Dimensional Analysis

Initially, the radius R of the blast should depend only on three fundamental quantities: the energy E released by the explosion, the time t after detonation, and the density ρ of the surrounding air.

Using dimensional analysis, the only combination of these quantities that produces the dimensions of length is the Sedov–Taylor relation:

R=C\left(\frac{Et^2}{\rho}\right)^{1/5}\qquad (1)

where:

R = radius of the expanding blast wave

E = energy released by the explosion

t = time after detonation

ρ = density of the surrounding medium

C = dimensionless constant determined by the physics of the explosion. For a strong spherical blast wave, C is approximately equal to 1.

Taking \rho to be 1.0 \, \mathrm{kg/m^3} (the measured air density at Trinity on the day of the test) and solving Equation (1) for E, we obtain an estimated yield of slightly more than 90 TJ.

Since 1 kiloton of TNT is equivalent to 4.184 \times10^{12} J, this corresponds to a yield of approximately 22 kilotons of TNT.

This is a remarkable result, considering the simplicity of the estimate: using only the explosion energy E, the elapsed time t, and the density of the surrounding air \rho, dimensional analysis reproduces the measured yield of the Trinity test with surprising accuracy.

There is a lesson to be learned. Sometimes the biggest secrets lie on the cover of a magazine.

The Trinity Test

Elsie McMillan remembers asking her husband Edwin what would happen at the Trinity Test.

REFERENCES

Trinity (nuclear test) — Wikipedia

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On This Day — US Detonates First Nuclear Weapon (Trinity Test, July 16, 1945) | The Magical World of Dimensional Analysis

“Humans destroyed Hiroshima, but humans also rebuilt it. This is a holy site … somewhere people can come to compare the horrors of the past with the city Hiroshima has become today.”

Kazumi Matsui
Hiroshima’s mayor

John von Neumann, John Wheeler, Hans Bethe, Robert Serber, Robert Marshak, Abraham Pais, J. Robert Oppenheimer, David Bohm, and Richard Feynman at the Shelter Island Conference of 1947.
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